Mexico’s confirmed coronavirus death toll surpassed India’s on Thursday to become the world’s third-highest, after months in which President Andrés Manuel López Obrador downplayed the virus as his government scrambled to control it.

As of Friday morning, Mexico had recorded 155,145 coronavirus deaths during the pandemic, according to a New York Times database. That is about 66,000 less than the official death toll in Brazil, the hardest-hit country after the United States.

Hospitals nationwide, particularly in Mexico City, are straining to provide beds and ventilators. Doctors are overwhelmed. People have been lining up to refill tanks of oxygen for relatives who are gasping for air in their homes.

Mexico has reported more than 1.8 million cases, and its caseload has surged since early December. The daily average number of new infections over the past week — 16,319 — was the seventh-highest in the world, just behind France.

The country’s death toll has been rising quickly, too, even as Mr. López Obrador insists that the end of the pandemic’s devastation is just around the corner. The average of 1,281 daily deaths in Mexico over the past week is higher than Britain’s and second only to the United States’.

And for all that, the disease’s true impact on Mexico is probably far worse than official figures indicate.

Testing levels are low, and many infected people are staying home because they distrust hospitals. A New York Times investigation found in May that the government was not reporting hundreds, possibly thousands, of coronavirus deaths in Mexico City.

When Mr. López Obrador said this week that he, too, had the virus, few Mexicans were surprised. He had spent months minimizing the pandemic by claiming that religious amulets protected him, for example, and refusing to wear a mask.

He has worked through his illness, saying on Monday that he had spoken with President Vladimir Putin of Russia. Mexico’s top epidemiologist, Hugo López-Gatell, told reporters on Thursday that Mr. López Obrador was experiencing minimal symptoms.

Some people in Mexico worry that Mr. López Obrador, 67, will go back to minimizing the danger of the coronavirus after he recovers with help from top-notch medical treatment, just as President Donald J. Trump did after a Covid-19 infection in October.

In Mexico City this week, Lilia Ramírez Díaz was making the second trip of the day to refill an oxygen tank for her father, who has diabetes and has been battling Covid-19 at home.

Both Mr. López Obrador and her father contracted the virus, she said in an interview, but the president “doesn’t have to go around looking and begging for an oxygen tank.”

The European Commission’s president has demanded that AstraZeneca provide a transparent and plausible explanation for why it will not be able to meet the delivery agreement of pre-ordered doses of its Covid-19 vaccine that is expected to be approved for use across the European Union on Friday.

The comments, by Ursula von der Leyen, come amid a dispute between the bloc and the pharmaceutical company, and hours before the commission made public a copy of its contract with AstraZeneca.

“There is a binding order, and the contract is crystal clear,” Ms. von der Leyen said in an interview with a German radio station earlier in the day. The contract includes language on two production facilities that can be used for making does intended for E.U. countries, she said, adding, “How they manage that is their affair.”

The comments come a week after AstraZeneca told the bloc that it would not be able to meet its commitment to begin deliveries of the 300 million doses of the vaccine. In the days since, a dispute between the British-Swedish pharmaceutical company and the bloc has escalated. The disagreement is fueled by concerns over a sluggish start to the vaccination campaign in its 27 member states, and has pitted Britain against the bloc, which it fully quit on Dec. 31 after years of wrangling.

The copy of the AstraZeneca contract that the European Commission released, which was heavily redacted, was largely similar to other industry contracts, including one that the bloc signed with CureVac. Although the AstraZeneca document includes legal language that protects the company over failures to deliver vaccines according to an agreed schedule, it also includes a clause saying that vaccines for this contract should be produced in factories within the European Union and in Britain.

The contract also says the company should make its best reasonable efforts to ensure the supply, or even switch to production outside the bloc and Britain if necessary. A detailed schedule of deliveries was redacted from the contract, which is under Belgian law.

The European Union has had several problems since it approved its first coronavirus vaccine, made by Pfizer and BioNTech, in December and then began a vast immunization campaign. It was already trailing weeks behind rich nations like the United States and Britain, and vaccine supplies have dwindled in recent days.

AstraZeneca’s plan to cut its deliveries as much as 60 percent deepened the troubles.

“What we want is a plausible explanation why there were these difficulties at the start,” said Ms. von der Leyen, herself a trained doctor.

She acknowledged that difficulties could happen in the highly complicated process of producing a safe vaccine under heightened time pressure, but noted that the European Union had invested a six-figure sum in AstraZeneca and other European pharmaceutical companies to enable pre-production.

“We wouldn’t have the possibility of the vaccine now had the E.U. not invested in these companies,” Ms. von der Leyen told Germany’s Deutschlandfunk radio on Friday. Other companies that received similar pre-orders, including for the Pfizer-BioNTech vaccine, have also faced production delays, but have offered reasonable explanations for the causes, Ms. von der Leyen said.

“What bothers us — by that I mean all 27 E.U. members,” she said, “is that AstraZeneca, unlike the other companies, cut supplies with very little notice and has not offered a plausible explanation of why the doses cannot be delivered.”

Even before Thursday, South Carolina stood out.

In a nation where new coronavirus cases were finally beginning to edge downward after a grueling two months, South Carolina remained stuck. Although its average number of new cases was decreasing, the state was recording the second-highest number per capita in the country, behind Arizona.

Then came news of the variant.

On Thursday, health officials in South Carolina said they had detected two cases of a more contagious coronavirus variant that first emerged in South Africa. It was the first report of that variant being detected in the United States, and raised questions about how many more variant infections may have gone undetected.

“That’s frightening,” Dr. Krutika Kuppalli, an infectious diseases physician at the Medical University of South Carolina in Charleston, told The Associated Press. “It’s probably more widespread.”

The variant, known as B.1.351, was originally identified in South Africa and has since been found in about 30 countries. It is not just more contagious, there is also evidence that vaccines are less effective against it.

The variant may pose a particular challenge for the United States, which conducts little of the genomic sequencing necessary to track the spread of new forms of the virus. And several variants have caused concern.

Among them are the B.1.1.7 variant first found in Britain and since seen in more than 46 countries and 24 U.S. states, and the P.1 variant, first found in Brazil, which officials in the United States reported having detected this week in Minnesota.

On Thursday, South Carolina’s Health Department said it had identified one case of the variant from South Africa the day before — when it was also notified of a second case by the Centers for Disease Control and Prevention.

The department said the cases involved no known travel to South Africa and no connection between the two patients, both of whom are adults. One was in the state’s Lowcountry region, in the south, and the other was in the Pee Dee region in the northeast.

That suggested that the variant is circulating in the community, and prompted a warning to the public to take precautions.

“The arrival of the SARS-CoV-2 variant in our state is an important reminder to all South Carolinians that the fight against this deadly virus is far from over,” Dr. Brannon Traxler, the health department’s interim public health director, said in a statement. “While more Covid-19 vaccines are on the way, supplies are still limited. Every one of us must recommit to the fight by recognizing that we are all on the front lines now.”

At an online briefing, Dr. Traxler said the same precautions were being taken for the new variant as for other virus cases. Both of the people who contracted the variant were tested in early January and have recovered, she said.

“We do not have concern at this time based on their contact tracing about there being the potential for any mass, widespread transmission,” Dr. Traxler said.

As of Thursday, there had been at least 431,169 cases and 6,903 deaths in South Carolina since the pandemic began.

Gov. Henry McMaster wrote on Twitter that the announcement was “important information for South Carolinians to have, but it isn’t a reason for panic.” He encouraged residents to wear masks and socially distance.

Johnson & Johnson said on Friday that its one-dose coronavirus vaccine provided strong protection against Covid-19, offering the United States a third powerful tool in a race against a worldwide rise in virus mutations.

But the results came with a significant cautionary note: The vaccine’s efficacy rate dropped from 72 percent in the United States to 57 percent in South Africa, where a highly contagious variant is driving most cases. Studies suggest that this variant also blunts the effectiveness of Covid vaccines made by Pfizer-BioNTech, Moderna and Novavax.

The variant has spread to at least 31 countries, including two cases documented in the United States this week.

Johnson & Johnson said it planned to apply for emergency authorization of its vaccine from the Food and Drug Administration as soon as next week, putting it on track to receive clearance later in February.

“This is the pandemic vaccine that can make a difference with a single dose,” said Dr. Paul Stoffels, the company’s chief scientific officer.

The company’s announcement comes as the Biden administration is pushing to immunize Americans faster even as vaccine supplies tighten. White House officials have been counting on Johnson & Johnson’s vaccine to ease the shortfall. But the company may have as few as seven million doses ready when the vaccine is authorized, according to federal health officials familiar with its production, and no more than 32 million doses by early April.

The variant from South Africa, known as B.1.351, could make the vaccine push tougher. Given the speed at which the variant swept through that country, it is conceivable that it could make up a large fraction of infections in the United States by April and therefore undermine the effectiveness of available vaccines.

The two vaccines approved by the U.S. government have been found to be less effective against the B.1.351 variant in clinical trials, a development that has unsettled federal officials and vaccine experts.

Many researchers say it is imperative to vaccinate people as quickly as possible. Lowering the rate of infection could thwart the more contagious variants while they are still rare.

“If ever there was reason to vaccinate as many people as expeditiously as we possibly can with the vaccine that we have right now, now is the time,” said Dr. Anthony S. Fauci, the government’s top infectious disease expert. “Because the less people that get infected, the less chance you’re going to give this particular mutant a chance to become dominant.”

global roundup

After months of delays, a team of World Health Organization scientists tracing the pandemic’s origin began its field work on Friday in Wuhan, the Chinese city where the coronavirus was first detected.

The W.H.O. said its team of 15 experts planned to visit hospitals, laboratories and a live animal market over the next several weeks in Wuhan, a city of 11 million, where the virus was detected in late 2019.

“As members start their field visits on Friday, they should receive the support, access and the data they need,” the W.H.O. said on Twitter. “All hypotheses are on the table as the team follows the science in their work to understand the origins of the #COVID19 virus.”

The Chinese government had repeatedly sought to delay the inquiry, apparently out of concern that the experts would draw attention to the government’s early missteps in handling the outbreak. But it relented under mounting global pressure.

The W.H.O. experts were first asked to undergo 14 days of quarantine in Wuhan, which ended on Thursday.

They plan to speak with some of the first patients to show symptoms of Covid-19, as well as with medical workers and Chinese scientists, according to the W.H.O. Their fieldwork will include a visit the Huanan Seafood Wholesale Market, where some of the first cases were detected.

They will also visit the Wuhan Institute of Virology and a laboratory operated by Chinese Center for Disease Control and Prevention.

The question of the pandemic’s origin has caused friction between China and the United States, with officials in each country at times blaming the other for unleashing the virus on the world.

Jen Psaki, the White House press secretary, said on Wednesday that the United States hoped for a “robust and clear” international investigation.

Chinese officials, in response, defended the country’s handling of the inquiry.

“We hope the U.S. side will work with China, take on a responsible attitude and respect facts, science and the diligent work of W.H.O. experts,” Zhao Lijian, a spokesman for the Chinese foreign ministry, said at a news conference in Beijing on Thursday.

• Chinese officials said on Friday that several passengers traveling to China from the United States had falsified coronavirus test results so they could gain entry to the country. The Chinese consulate in San Francisco said the passengers had “changed their test results from positive to negative” and that other travelers had lied about test results. The consulate did not provide details about the passengers or the punishments they might face. China maintains strict border control rules, including a requirement that travelers present results from antibody and nucleic acid tests before they fly. The consulate said the passengers had violated public health laws. “The way they put others at risk is odious,” the statement said.

• Vietnam recorded nine more coronavirus cases on Friday, including one in the capital, Hanoi, as a new outbreak spread beyond the two northern provinces where infections had first been detected a day earlier. Officials put the number of cases from the latest outbreak at 93 as of Friday afternoon but said that it could reach 30,000, nearly 20 times the number of cases that Vietnam detected during the entire first year of the pandemic. Vietnam has been among the most successful countries in containing the virus, with strict border controls, mask-wearing, contact tracing and isolation of infected people. The latest outbreak comes as officials from the governing Communist Party meet to select the country’s new leaders, an event held once every five years.

• Hungary’s medicine authority has approved the coronavirus vaccine developed by the Chinese company Sinopharm. “This means that in addition to Pfizer, Moderna, Sputnik and AstraZeneca, we can also count on Sinopharm,” said Dr. Cecilia Muller, the country’s chief medical officer. “We trust that these vaccines will be readily available in large quantities and the immunization process will be completed in larger numbers in less time.”

  Regarding the options, Prime Minister Viktor Orban expressed enthusiasm for the Chinese vaccine on Friday. “I will wait for the Chinese vaccine,” he said. “I trust that one the most.”

A Washington hospital system apologized after The Seattle Times reported that it had offered vaccines to wealthy donors while others went without the coveted shots.

Overlake Medical Center & Clinics sent an email to about 110 donors who gave more than $10,000 to the hospital system, telling them they could register for open appointments “by invite” only.

The report drew a rebuke from Gov. Jay Inslee, who said during a news conference on Tuesday that the practice was “simply unacceptable.”

Overlake’s president and chief executive, J. Michael Marsh, apologized in a statement, adding that even those donors would have been required to show that they were eligible for the vaccine under state guidelines.

“We recognize we made a mistake by including a subset of our donors and by not adopting a broader outreach strategy to fill these appointments, and we apologize,” Mr. Marsh said.

The hospital’s conduct mirrors that of other facilities that have made news for prioritizing wealthy donors over the rest of the population. A Florida nursing home and assisted-living facility called MorseLife Health System came under investigation after The Washington Post and The New York Post reported that it had prioritized its donors as well.

Another, Baptist Health in Miami, invited a donor to get a shot. The recipient said she believed she was offered a vaccine because she had donated and volunteered for the hospital.

And in Jefferson City, widespread confusion led some Missouri lawmakers to scramble for shots that were not intended for them. Group texts among House members and employees said vaccines were available at an area hotel, but the shots were meant for the state’s public safety and transportation employees.

Mr. Inslee said during Tuesday’s news conference that Washington State’s biggest barrier to widespread vaccine distribution was supply. As of Thursday, 6.2 percent of the state’s population had received their first dose. Just 1.2 percent had received the full two doses.

After hearing of the prioritizing of donors, Mr. Inslee said he believed that the hospital had halted that practice.

“We have to maintain public credibility in this system,” he said.

With pressure mounting to get Covid-19 vaccine doses into arms as quickly as possible, many overburdened city health departments across the country have turned to partnerships with hospitals, nonprofit organizations and pharmacies. In Philadelphia this week, one such deal went awry after the city leaned on a start-up led by college students who were eager to get involved but had little experience.

The start-up is an organization called Philly Fighting Covid, which was founded last year by a 22-year-old graduate student, Andrei Doroshin. The group quickly won plaudits for volunteering to run free testing sites and for using 3-D printers to make face shields that it supplied free to health care workers.

So when Philadelphia began receiving shipments of vaccine and needed help administering doses on a large scale, the city health department turned to Philly Fighting Covid to operate what would be the largest vaccination site in the state, at the Pennsylvania Convention Center.

It took less than three weeks after vaccinations began for the partnership to sour.

Since it opened on Jan. 8, the site has vaccinated nearly 7,000 people, though there were reports in local media that appointments had been overbooked and some people were turned away. Mr. Doroshin attributed those problems to issues with an online sign-up system that allowed thousands of ineligible people to register for appointments.

Then on Tuesday, the city health commissioner, Thomas Farley, said at a news conference that the health department would no longer work with Philly Fighting Covid. The city learned, he said, that the group had unexpectedly canceled its testing efforts to focus on vaccination; that it planned to change from nonprofit status to a for-profit company; and that it had changed its data privacy policy to allow it to potentially sell data about patients to third parties, a step first reported by the public radio station WHYY.

“We did not think that was appropriate,” Dr. Farley said about the data policy. “We thought, ‘If there’s any attempt to do this, even the possibility, then people won’t trust this organization.’”

In an interview, Mr. Doroshin said his group had only the best intentions, but he acknowledged its inexperience.

“We’re a bunch of kids,” Mr. Doroshin said. “I didn’t know anything about legal structure before this. I didn’t care. I’m not a lawyer, I’m a nerd. People are trying to make me out to be this nefarious thing. I’m like, ‘Dude, I didn’t know all the rules of a nonprofit organization until I did this.’”

He said that the company had decided to switch to a for-profit structure in order to expand quickly, and that it had not hid its intentions from the city.

Mr. Doroshin did acknowledge that there were problems with the organization’s privacy policy, which he said had been posted in haste. But he said that the group had not sold or otherwise disseminated any of the patient data it collected, and that the posted policy “was frankly just a mistake.”

Katrina Lipinsky, a registered nurse who volunteered at the group’s vaccination site, said in an interview that at the end of one day, after the group tried to find takers for a number of leftover doses, she saw Mr. Doroshin put a few in his backpack, along with the vaccination cards that are used to track vaccination timelines. She said she had reported it to city investigators.

“Obviously, that didn’t seem right,” she said.

Dr. Farley, the health commissioner, told reporters that any leftover vaccine doses should have been given back to the health department. He said the department was looking into the matter.

“If that’s true, that’s very disturbing,” he said. “They shouldn’t have done that.”

In the interview, Mr. Doroshin acknowledged that he had taken four doses home with him and administered them to friends. He said that he should have had a nurse present when he gave the shots, but that he did not regret making use of doses that would otherwise have expired that night.

“I’m OK with being a person that broke a rule to not have any vaccine left over,” he said. “If that’s the final word I have in my book, then that’s OK. I’m OK with dying with that.”

Dr. Anthony S. Fauci, addressing more than 6,000 American teachers in a video meeting, said Thursday evening that students need to return to the classroom for the country to begin recovering.

“We are not going to get back to normal until we get the children back in school, for the good of the children, the good of the parents and the good of the community,” he said.

Attending a meeting convened by the two national teachers unions, Dr. Fauci brought with him the message of the Biden administration: that all K-8 schools should aim to reopen within the next 100 days. He said they can expect support from Washington in the form of a new stimulus package to fund sanitation upgrades and other safety measures.

As of last month, about one third of American school districts were operating entirely remotely, and Dr. Fauci acknowledged that “mitigating factors” may make the 100-day goal difficult to achieve in some places.

Fielding questions submitted by educators, he did not hesitate to acknowledge potential dangers.

He discussed the emergence of new variants of the coronavirus that appear more contagious and more resistant to vaccines. And he said that while he expected vaccines to prevent inoculated teachers from passing the virus onto their loved ones, there was not yet concrete evidence that would be the case.

As Dr. Fauci spoke, educators at the meeting posted comments — many reflecting frustration and anxiety. They complained that many states had not prioritized teachers for vaccination and said students were not able to effectively stay masked throughout the school day.

Several called for job actions.

“Teachers need to participate in a national strike to protect kids, communities, and teachers,” one wrote.

Dr. Fauci appeared alongside two powerful teachers union presidents: Randi Weingarten of the American Federation of Teachers and Becky Pringle of the National Education Association.

The event took place as some local unions across the country, most notably in Chicago, continue to resist efforts to reopen schools, arguing that doing so before widespread teacher vaccination would risk lives.

Ms. Weingarten has staked out a somewhat more moderate position, arguing that schools can operate safely before teachers are vaccinated by using strategies such as surveillance testing for the virus and updating ventilation systems. She has also asked for teachers with health concerns, or who live with family members with compromised immune systems, to be allowed to continue to work remotely.

Rabbi Chaim Kanievsky, 93, can’t use a phone. He rarely leaves his house. His family says he has never successfully made a cup of tea. His closest aides think he doesn’t know the name of Israel’s prime minister. He studies the Torah for, give or take, 17 hours a day.

Yet despite his apparent detachment from worldly life, Rabbi Kanievsky has become one of the most consequential and controversial people in Israel today.

The spiritual leader of hundreds of thousands of ultra-Orthodox Jews, Rabbi Kanievsky has landed at the center of tensions over the coronavirus between the Israeli mainstream and its growing ultra-Orthodox minority.

Throughout the pandemic, the authorities have clashed with the ultra-Orthodox over their resistance to antivirus protocols, particularly their early refusal to close schools or limit crowds at religious events. Similar conflicts have played out in the New York area.

Rabbi Kanievsky, issuing pronouncements from a book-filled study in his cramped apartment in an ultra-Orthodox suburb of Tel Aviv, has often been at the fore of that resistance. Twice, during the first and second waves of the pandemic in Israel, he rejected state-imposed antivirus protocols and did not order his followers to close their yeshivas, independent religious schools where students gather in close quarters to study Jewish Scripture.

“God forbid!” he exclaimed. If anything, he said, the pandemic made prayer and study even more essential.

Both times he eventually relented, and it is unlikely that he played as big a role in spreading the virus as he was accused of, but the damage was done.

Many public health experts say that the ultra-Orthodox — who account for about 12 percent of the population but 28 percent of the coronavirus infections, according to Israeli government statistics — have undermined the national effort against the coronavirus.

The reaction has been fierce, much of it centered on Rabbi Kanievsky.

The rabbi “must be arrested for spreading a disease,” blared a column last week in Haaretz, a left-wing newspaper. “This rabbi dictates the scandalous conduct in the ultra-Orthodox sector,” said an article in Yedioth Ahronoth, a centrist news outlet.

The backlash exaggerates both the rabbi’s role and that of the ultra-Orthodox in general. Ultra-Orthodox society is not monolithic, and other prominent leaders were far quicker to comply with antivirus regulations.

Ultra-Orthodox leaders say most of their followers have obeyed the rules, although their typically large families, living in tight quarters under what is now the third national lockdown, have inevitably contributed to the spread of the contagion.

Rabbi Kanievsky’s position has also been more nuanced than sometimes portrayed. But he has nonetheless contributed to one of the biggest-ever showdowns between the Israeli mainstream and the ultra-Orthodox.

With the pandemic exposing racial disparities in the United States — Black people have died of Covid-19 at nearly three times the rate of white people, according to the Centers for Disease Control and Prevention — health officials have been working to promote vaccinations in Black communities, and to combat doubt.

So doctors in Atlanta turned to Tyler Perry — a popular and prolific actor, director and studio head — to spread the word to Black audiences that the vaccine was harmless. He agreed to interview the experts, turning it into a TV special that aired Thursday night on BET. On the show, he peppered doctors from Grady Health System with questions about the safety of the vaccine, how it was developed, how it was tested and how it works.

At the end of the interview, with his sleeve pulled up, Perry got the jab as cameras rolled.

Perry is one of the most powerful people in the entertainment industry. He built his fortune portraying the character of Madea, a tart-tongued and irreverent matriarch, onstage and onscreen, before retiring her in 2019 to concentrate on other projects, which include running his 330-acre studios in Georgia.

Skepticism about the Covid-19 vaccine among Black people has been deeply concerning to health officials. A recent study by the Kaiser Family Foundation found that one in three Black people was hesitant about vaccine. A recent CNN analysis found that Black and Latino Americans were getting the vaccine at significantly lower rates than white people — rates attributed to, among other factors, lack of access to health care for many Black people, but also to an entrenched mistrust about the medical establishment.

On the BET special, Perry spoke of episodes in history that have led to a lack of faith in the medical establishment and the government, among them the Tuskegee Syphilis Study, in which doctors allowed syphilis to progress in Black men by withholding treatment from them, and the case of Henrietta Lacks, a Black woman who died of cervical cancer in 1951, whose cells were used in research without her knowledge or consent.

“We as Black people have healthy hesitation when it comes to vaccinations and so on and so forth, and even disease,” he said.

Perry said he didn’t want people getting vaccinated just because he had. “What I want to do is give you the information, the facts,” he said. “There’s a lot of misinformation out there.”