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Mr. Abbott’s order has limited exceptions for young children, people with medical conditions and people eating in restaurants or exercising outdoors.

Mr. Abbott had previously cast his opposition to mask mandates as a matter of principle. Last month, in an interview with KWTX-TV, Mr. Abbott said that while businesses could be ordered to require masks, “we want to make sure individual liberty is not infringed upon by government, and hence government cannot require individuals to wear masks.”

The governor also said that with limited exceptions Texans cannot gather in groups larger than 10 people and must maintain six feet of social distance from one another.

Even the aging rapper Vanilla Ice has yielded to pleas from local health officials, backing off a planned July 4 concert at Lake Travis in Texas. He said on Thursday that he “didn’t know the numbers were so crazy.”

Gov. Abbott’s decision was the latest sign that Republicans are embracing masks, as the virus spreads in a number of Republican-led states in the South and the West. Vice President Mike Pence pointedly wore a mask at a church visit in Dallas on Sunday. Even President Trump, who has resisted wearing a mask in public, said this week, “I’m all for masks,” while still declining to wear them.

Key Data of the Day

June was the month the pandemic spiraled out of control in the U.S. July may show how bad it can get.

On June 1, Florida officials announced 667 new cases. On July 1, they added more than 6,500. Today they reported over 10,100, a record.

In Texas, there were 1,100 new cases at the start of last month. On Wednesday, more than 8,100. In Georgia, it went from 700 to 2,300. And in California, where some newly reopened businesses were again being shut down, new cases went from about 2,500 to 7,600.

If June was the month when the pandemic spiraled from America’s grasp, July seems destined to be month when the country will learn just how bad it will get.

The United States reported nearly 50,000 new cases on Wednesday, the fifth single-day case record in eight days, as the nation staggered toward a holiday weekend burdened by a pandemic that is only growing worse.

Although Trump administration officials have argued in recent weeks that the rise in cases can be attributed to increased testing, Adm. Brett P. Giroir, the assistant secretary of health who is overseeing the government’s testing response, told Congress on Thursday that the higher numbers in fact reflect an increase in cases.

“There is no question that the more testing you get the more you will uncover, but we do believe this is a real increase in cases because the percent positivities are going up,” Admiral Giroir said. “So this is real increases in cases.”

Though single-day snapshots are an imperfect measure of the pandemic, the broader picture is also exceedingly bleak. Case numbers were trending upward in 38 states as of Wednesday. The problem spots in the country’s South and West were spreading north and east, and hospitalizations surged in some states.

In Kansas, the state health secretary blamed lax social distancing for his state’s spike and predicted that increases were likely to continue. In Pennsylvania, Gov. Tom Wolf signed an expanded order to wear masks. And in Michigan, where cases have started inching upward again and where more than 100 infections were traced to a single bar, Gov. Gretchen Whitmer ordered bars to cease indoor service again in much of the state.

“If we want to be in a strong position to reopen schools for in-person classroom instruction this fall,” Ms. Whitmer said in a statement, “then we need to take aggressive action right now to ensure we don’t wipe out all the progress we have made.”

In Arizona, which Mr. Trump visited in May and praised for its reopening plans, Gov. Doug Ducey decided this week to close the state’s water parks and to order bars, gyms and movie theaters to close for 30 days. On Wednesday, Mr. Pence visited Arizona to discuss the crisis.

Mr. Pence told Mr. Ducey that the federal government would help the state with a request for 500 additional public health personnel by mobilizing doctors, nurses and technical personnel.

In Nebraska, state leaders suggested that holiday cookout hosts keep guest lists to make contact tracing easier if there is an outbreak. The Oregon Health Authority warned residents that “the safest choice this holiday is to celebrate at home.”

Elsewhere, the pleas were similar: Skip the party. Stay home. Don’t make a bad situation worse.

Young patients are dying, too, particularly obese ones, a W.H.O. official says.

As the number of infections soars in some countries, the mortality rate has not kept pace. Some believe that the increased number of young people getting infected may account for the disparity.

But Dr. Soumya Swaminathan, chief scientist of the World Health Organization, said on Thursday that young people are vulnerable to severe complications, especially if they are overweight.

“We should not become complacent that it’s fine for young people to get infected,” Dr. Swaminathan said, “because there is a subset, particularly those with obesity, those with habits like smoking, for example, who are at higher risk of complications and death.”

She also said that determining death rates in the midst of the pandemic is complicated by several factors. One is the lag time between the identification of a case and death.

Fatalities from Covid-19, the disease caused by the virus, typically occur three to five weeks after patients are infected. But many countries divide the number of deaths by the number of infections.

“It has been suggested by scientists that, really to get an accurate idea of case fatality rates, you should divide by the number of cases two weeks ago, not the number of cases today,” Dr. Swaminathan said.

The death rate in the United States is about 5 percent. But according to recent data from the C.D.C., there are likely 10 times more infections than are reported. The so-called infection fatality rate — which includes all cases, not just identified cases — may be about 0.6 percent globally, Dr. Swaminathan said.

Locked down with their abusers, women in the U.K. can expect little help from the government.

The British government failed to heed early warnings that domestic abuse would soar during the lockdown. Now, more than four months later, it is still lagging in its response.

For some victims trapped with their abusers, the consequences have been catastrophic.

In the first month after the lockdown began in late March, 16 women and girls were killed in suspected domestic homicides — more than triple the number in the same period in 2019. At least 10 more have died in the two months since then.

Distress calls to abuse hotlines are soaring, charities are overwhelmed and some emergency housing providers cannot meet demand.

The courts offer limited help, at best. Overwhelmed by lengthy delays, they have allowed some accused of abuse to return home, despite restraining orders.

Other countries have fared better.

New Zealand included domestic abuse preparations in its lockdown planning from the start. Italy, Spain and other countries set up nationwide programs to house abuse victims in hotels if existing shelters were full. Germany made an open-ended pledge to fund shelters and other services.

Britain did none of this.

Interviews with more than 50 government and law enforcement officials, academic experts, front-line support workers and abuse survivors show that British leaders never prioritized domestic abuse in lockdown planning and are still failing to quickly provide help.

“There is no defined government strategy at all,” said Jess Phillips, a Labour lawmaker who speaks for the opposition on domestic violence policy. “Some services have got no funding to keep going.”

The government contests that. Victoria Atkins, the minister in charge of the government’s response to domestic violence, said in a statement that the authorities were “committed to supporting victims and bringing perpetrators to account.”

Congress eyes more spending as the virus surges and the economy falters.

But there is little consensus on what the next aid package should look like and how quickly it will arrive.

Some economists say lawmakers are risking further damage to an already fragile recovery by not moving more quickly. Real-time indicators of shopping patterns and business openings suggest that a once-brisk economic rebound stalled in June as the virus began spreading more rapidly in Texas, Florida and other states. And even the most encouraging signs of recovery — such as the jobs report released today, which said U.S. payrolls grew by 4.8 million in June — underscore how far the recovery still has to get back to what was normal before the virus: Nearly 18 million Americans remain unemployed.

Lobbyists and lawmakers say the Trump administration, which has lost several economic advisers in recent weeks, is not deeply engaged in devising another rescue package. Officials have hinted for weeks that they would formally propose tax cuts, infrastructure spending and other initiatives, but they have not followed through. Mr. Trump has expressed support for additional tax cuts and government spending.

Senators are expected to leave Washington on Thursday after making only incremental progress toward an agreement to extend further relief to businesses and laid-off workers who are about to lose or have already exhausted federal assistance.

“The stimulus was very short-lived,” said Aneta Markowska, chief economist at the investment bank Jefferies. “This problem is going to persist long beyond July.”

Only a dozen states have managed to keep new case levels flat or declining.

As the virus has exploded in large swaths of the nation over the past two weeks, only a dozen states, mostly in the Northeast, have managed to keep new case levels flat or declining.

New York, which averaged 9,877 cases per day when it reached the height of its outbreak in April, has been staying mostly flat at an average of 620 cases per day. Other states in the Northeast that were initially hit hard, including New Jersey, Connecticut, Massachusetts and Rhode Island, are all plateauing at far lower levels than earlier in the pandemic.

Massachusetts announced Thursday that it would move forward with the next phase of its reopening on Monday for all areas of the state except for Boston.

Movie theaters, outdoor performance venues, fitness centers, museums and other businesses will be allowed to resume operations. Up to 25 people will be allowed to gather in indoor spaces, provided that they are adequately spaced. Boston is scheduled to ease its restrictions in those areas on July 13.

“Today the public health data makes clear that Massachusetts is effectively bringing the fight to the virus as we’ve reopened,” Gov. Charlie Baker said at a news conference Thursday.

Other states where new cases have stayed largely the same over the past two weeks, according to a New York Times database, include Vermont, Maryland, Virginia, Indiana, Nebraska and South Dakota.

The state showing the biggest decline in new cases over the past two weeks, according to the database, was New Hampshire. Its decline has been modest: It is now averaging 29 new cases a day, down from over 34 cases a day two weeks ago.

But its governor, Christopher T. Sununu, said that the state should not expect its declines to last.

“I actually think a spike in Covid cases will happen in New Hampshire, and that is the real tough situation that we have,” he said Wednesday on WMUR. “It would be very ignorant and arrogant of us to think that we are going to be completely immune to what’s happening in other parts of the country.”

“The reason the spikes are happening in other parts of the country aren’t just because they’re reopening,” he said, adding that many people in other areas, and particularly young people, were not wearing masks or practicing social distancing.

“Unfortunately I think we are going to see some outbreaks here,” he said. “The key is here we can manage it this time: We have P.P.E., we have testing capabilities, we have more financial resources.”

Florida reports over 10,100 new cases. Contact tracers are feeling overwhelmed.

Florida reported Thursday that an 11-year-old boy in Miami-Dade County had died, the youngest death attributed to Covid-19 in the state.

Vice President Mike Pence visited the state Thursday and met with Gov. Ron DeSantis to discuss the state’s rapidly worsening outbreak. The visit was quite different in tone from one in May, when the two men ate, unmasked, at a burger bar and Mr. Pence praised the state’s reopening plans, saying, “I really think Florida has set the pace.” Back then Mr. DeSantis proclaimed “we’ve succeeded,” and added, “I think that people just don’t want to recognize it because it challenges their narrative.”

On Thursday, both men wore masks, but removed them to speak at a news conference, and Mr. Pence said that the federal government would work with the state to help flatten its curve. “The economic comeback that is underway is a demonstration that we don’t have to choose between opening up America and the health of our people: We can do both,” he said. “And that’s the challenge that we face today across the Sun Belt.”

Contact tracers, unable to keep up with so many new cases, have become overwhelmed by the surge.

“We are starting to lose the ability to do contact tracing,” said Dr. J. Glenn Morris, director of the Emerging Pathogens Institute at the University of Florida.

City and county officials desperate to stop the spread have adopted local mask mandates and closed the beaches over the holiday weekend. Some communities are deploying teams of public employees to go door-to-door in the hardest hit neighborhoods, distributing masks, hand sanitizers and fliers with information on symptoms and testing.

Testing demand has remained high: In Miami-Dade County, which has averaged more than 1,400 daily cases, the biggest testing sites begin taking appointments at 9 a.m. for the next day and have filled them by 9:30 a.m., county officials said. “The requests for testing have exploded,” said Maurice Kemp, county deputy mayor.

Elsewhere in the United States:

• Five of the nine Atlantic City casinos are reopening Thursday but with new rules: Gamblers must wear masks, and won’t be allowed to smoke, drink or eat inside.

• In New York City, Mayor Bill de Blasio announced on Thursday that the vast majority of families have indicated that they want to send their children back to school in September, according to a survey of roughly 450,000 families. The city is still working on plans to safely maximize the number of students in schools, he said, adding that schools could shift to a staggered schedule. The governor has said logistics are up to individual districts.

• Also in New York City, 22 streets, some already closed to car traffic, will be dedicated to outdoor dining on Friday nights and weekends. The move will be key in “some places in the city where we have extraordinary restaurants concentrated in one place,” the mayor said.

• Officials rushing to contain a virus cluster tied to a party in a New York City suburb used an unusual legal strategy: issuing subpoenas to partygoers.

• Herman Cain, a former Republican presidential candidate, announced Thursday that he had been hospitalized with the virus. Mr. Cain, who attended Mr. Trump’s indoor rally in Tulsa, Okla., on June 20, learned Monday that he had tested positive, was hospitalized Wednesday and on Thursday “was resting comfortably in an Atlanta-area hospital,” according to a statement posted on his Twitter account.

• Officials in Montana announced on Thursday more than 60 new cases, a single-day high. After weeks with little virus activity, including several days in May when no new cases were identified, Montana surpassed 1,000 total cases this week.

• McDonald’s announced a three-week pause in its plans to resume dine-in service at thousands of locations across the United States.

California’s governor again implores residents to wear masks.

Noting what was probably his last chance to reach residents before the July 4 holiday, Gov. Gavin Newsom of California on Thursday implored residents to refrain from gathering with people outside their household — no matter how great the temptation — and to wear masks.

“The evidence is simply overwhelming,” he said in a video news conference. “Masks keep Californians healthy.”

Mr. Newsom unveiled a new public awareness campaign about the importance of wearing masks, having already ordered people to wear them in most indoor — and some outdoor — public settings.

But amid rising case counts and hospitalizations, the governor was peppered with questions about how the state will actually enforce newly announced restrictions across counties where local leaders have shown varied willingness to comply with state-issued directives.

That particularly applied to 19 counties, home to almost three quarters of the state’s population, where the spread of the virus has been the most disturbing.

“We are working with counties in the spirit of partnership,” Mr. Newsom said. “But if we don’t see the level of local action that we are hoping for, with all 19 coming into compliance, that hand will be forced.”

On Wednesday, he announced that he was establishing teams to work with local authorities. The governor has emphasized that $2.5 billion in pandemic aid will be reserved for counties that do their share of enforcement. Nevertheless, he said, “it requires some level of personal responsibility.”

“The most important thing we’ve learned over the past couple of months is that we should focus on how, not when, to safely reopen,” Mr. Newsom said.

The state on Thursday reported thousands of new cases, he said. Over the past two weeks, he said, the rate of positive tests had increased to 6.3 percent, as hospitalizations increased by 56 percent and intensive care cases rose by 49 percent.

Researchers find new evidence that a mutation helped the virus spread, but questions linger.

For months, scientists have debated whether a variant of the virus that has come to predominate in much of the world did so partly because it is more transmissible than other viruses. On Thursday, a team of researchers reported new evidence suggesting that the variant did have such an advantage.

The new paper, led by Bette Korber, a theoretical biologist at Los Alamos National Laboratory, and posted by the journal Cell, presents evidence in the form of lab findings, tests of infected patients and a broad statistical analysis of the pandemic as the D614G variant took over in cities, regions and countries. “The consistency of this pattern was highly statistically significant, suggesting that the G614 variant may have a fitness advantage,” the authors concluded.

The underlying question is important for understanding the early phases of the pandemic and anticipating how it will progress in the coming months. If the genetic glitch that defines the variant imparted even a slight increase in transmissibility, it would help explain why infections exploded in some regions and not in others with similar density and other attributes.

Skeptics argue that it is far more likely that the variation spread widely by chance, multiplying outward from explosive outbreaks in Europe.

“This is an extraordinarily challenging problem,” said Dr. Marc Suchard, a biostatistician at the University of California, Los Angeles, School of Medicine. “The evolution and demography are complex. So there’s much more work to be done.”

Dozens of fraternity members test positive for the virus at the University of Washington.

At least 80 students living in fraternity houses at the University of Washington have tested positive for the virus, the university confirmed on Thursday.

The university set up a testing facility on Monday within walking distance of Greek Row in Seattle, and more than 800 people have been tested so far, said Michelle Ma, a university spokeswoman.

By Tuesday, the school had confirmed that 38 students living in 10 fraternity houses had tested positive. The larger number comes from the Interfraternity Council, a student-run governing body, according to Erik Johnson, the president of the council. Mr. Johnson said that the 80 students from 12 houses self-reported their positive test results to the presidents of their chapter facilities.

Many universities around the country are grappling with how to safely reopen, as dormitories and other communal spaces pose unique safety challenges.

Public health experts also say that college-town bars, nightclubs and corner taverns are becoming dangerous new hot spots for the coronavirus, seeding infections in thousands of mostly young adults and adding to surging cases nationwide. At least 100 new cases have been linked to Harper’s Restaurant and Brew Pub, a popular spot in the college town East Lansing, Mich., since it reopened in June.

“What is occurring north of campus provides lessons for students as they consider their return to campus this fall,” Dr. Geoffrey Gottlieb, the chair of the University of Washington’s Advisory Committee on Communicable Diseases, said in a statement. “If everyone does their part to keep each other safe, we can continue to engage with one another and with our studies in the university environment by wearing face coverings and remaining physically distant.”

More than 1,000 students live in 25 fraternity houses in the neighborhood north of the university’s Seattle campus. The school says it has asked infected students to self-isolate.

Global roundup

Tokyo’s nightlife districts see a surge in new cases.

Cases had been rising over the last week, with a high concentration detected in the city’s nightlife districts.

In a news conference on Thursday, Yuriko Koike, the Tokyo governor, said that people in their 20s and 30s accounted for 70 percent of the cases and that many were asymptomatic.

Ms. Koike said she would not ask businesses to close but encouraged the public to take precautions.

Dr. Norio Ohmagari, director of the Disease Control and Prevention Center at the National Center for Global Health and Medicine, said the average daily number of cases, whose route of infection could not be traced, had more than doubled in the last week.

“It indicates the possibility that community transmission could be spreading,” he said.

Elsewhere in the world:

• Days after a wedding in India, the groom died, and at least 100 guests tested positive for the virus. Indian officials have opened an investigation into the mid-June gathering, which some experts are calling a superspreader event, attended by more than 300 guests in the city of Patna, in the northeastern state of Bihar.

• The pandemic crushed the tourism industry in Venice and other over-visited cities. But many see this as an opportunity to rethink a “tourism monoculture.”

• In recent weeks, Brazil has emerged as one of the world’s most severe hot spots, second only to the United States. With Brazil’s caseload ballooning, Ernesto Londoño, the Brazil bureau chief for The New York Times, explains what went wrong.

• The European Centers for Disease Control and Prevention urged European Union countries to step up testing and contact tracing, and asked governments to communicate to their citizens that “the pandemic is not over.” The warning comes as Europe’s reopening has brought a resurgence of cases in some pockets.

A lockdown is reimposed in the West Bank after a steep rise in cases.

The Palestinian Authority announced plans to reimpose virus restrictions throughout the West Bank following a sharp rise in the number of new cases in the territory.

Ibrahim Milhim, a spokesman for the authority, said during a Wednesday news conference that all areas of the West Bank would be locked down for five days beginning on Friday. All businesses will be closed with the exception of bakeries, supermarkets and pharmacies.

A total of 2,908 people in the territory have contracted the virus since the beginning of March — and more than 2,200 of those cases came in the past two weeks alone, according to the health ministry of the Palestinian Authority. The number of virus-related deaths in the territory climbed from three to eight in the same period.

More than 80 percent of the current cases are linked to the city of Hebron, which began to shut down on Wednesday evening.

Mr. Milhim said that the five-day lockdown could be extended and called on Palestinians to follow social distancing guidelines and wear masks, warning that there would be consequences for those who did not comply.

Reporting was contributed by Rachel Abrams, Livia Albeck-Ripka, Aliza Aufrichtig, Julie Bosman, Benedict Carey, Ben Casselman, Stephen Castle, Emily Cochrane, Michael Cooper, Jill Cowan, Steven Erlanger, Richard Fausset, Luis Ferré-Sadurní, Kimiko de Freytas-Tamura, Thomas Fuller, Jenny Gross, Jack Healy, Makiko Inoue, Annie Karni, Isabella Kwai, Ernesto Londoño, Patricia Mazzei, Mark Mazzetti, Giulia McDonnell Nieto del Rio, Jesse McKinley, Sarah Mervosh, Anna Momigliano, Monika Pronczuk, Adam Rasgon, Motoko Rich, Amanda Rosa, Nelson D. Schwartz, Dionne Searcey, Ed Shanahan, Eliza Shapiro, Mitch Smith, Jim Tankersley, Sabrina Tavernise, Hisako Ueno, David Waldstein, Caryn A. Wilson, Edward Wong, Sameer Yasir and Karen Zraick.