More states are detecting the highly contagious virus variant.

Thursday began with a warning, and it was soon borne out.

“We believe things will get worse as we get into January,” Dr. Anthony S. Fauci, the United States’ top infectious disease specialist, said in a radio interview at the start of the day.

It didn’t take long for him to be proved right: Things immediately got worse.

For the second day in a row, the United States set a record for daily reported deaths: at least 4,111. And public health officials recorded a new daily case record, too: at least 280,028 new infections. (That excludes two days with figures driven up by reporting anomalies, and it is possible that the new highs in deaths and cases may reflect reporting lags tied to the holidays.)

The figures were an uncomfortable reminder that while many Americans were fixated on the political events roiling Washington, the pandemic hadn’t ceased wreaking havoc across the country.

With hopes buoyed by the arrival of a vaccine, and then dimmed by the delays in rolling it out, Dr. Fauci urged Americans to be patient. In his interview with NPR, he said that any program so large in scale would hit stumbling blocks. And the holiday timing of the rollout may have added to the delays, he said.

“I think it would be fair to just observe what happens in the next couple of weeks,” Dr. Fauci said. “If we don’t catch up on what the original goal was, then we really need to make some changes about what we’re doing.”

Dr. Francis S. Collins, director of the National Institutes of Health, also said it was not surprising that the vaccine drive had gotten off to a “rocky” start.

“That’s a lot of logistics,” he told The Washington Post. “So maybe we shouldn’t be too shocked that it didn’t go like clockwork.”

And, in fact, after a lagging start, vaccinations were beginning to speed up.

In the third week of the drive, more people were reported to have received their initial shots than in the first two weeks combined. The government count rose by 470,000 from Tuesday to Wednesday, and then by another 612,000 from Wednesday to Thursday.

Edward Goldberg’s phone would not stop ringing. Not only was the concierge doctor on Manhattan’s Upper East Side fielding calls from patients who went to St. Bart’s or Aspen — the wisdom of public-health officials be damned — and came back with Covid, he was hearing from healthy people too. They had an urgent desire for the coronavirus vaccine, and surely there was a way to gain access to it immediately.

Another contingent was calling Dr. Goldberg’s office inquiring about membership in his practice, assuming that they would then be fast-tracked for the vaccine. Concierge medicine involves the payment of annual fees — in Dr. Goldberg’s case, $20,000 a year — for what is essentially unlimited access to a doctor’s care. When asked how quickly someone might receive a vaccine, Dr. Goldberg explains that New York State is levying huge penalties against any medical outfit that tries to game the protocols for distribution.

It was inevitable that in an era marked by inequity and radically conflicting interpretations of truth that the rollout of the Covid-19 vaccine would be marked by so much delusion on multiple fronts. On the one hand are the rich, who are accustomed to finding workarounds whenever they want something that is in short supply and see little need for a different approach when it comes to protecting themselves from a disease that has largely devastated the underclass.

And then there are the skeptics who believe that the vaccine is trouble. In a survey of 1,117 Americans, conducted in early December, a quarter of respondents said they would not take the vaccine when it became available to them, while another quarter said that they were not sure.

A little over a week ago, Lara Devgan posted a video of herself getting the vaccine on Instagram. A Park Avenue plastic surgeon, she’d been hearing from some of her patients — those who have had cosmetic fillers — that they were worried the vaccine would cause temporary facial swelling.

“As someone who performs injectable facial fillers — who likes them and uses them myself — I believe the vaccine is safe,’’ Dr. Devgan said, “and the concept about worrying about how your face looks is not a reason not to get the vaccine.”

In a boost to Israel’s vaccination campaign, Prime Minister Benjamin Netanyahu announced on Thursday that he had reached an agreement with Pfizer that will enable all Israelis above age 16 to be inoculated against Covid-19 by the end of March.

Mr. Netanyahu made the remarks hours before Israel was set to tighten its current lockdown. Health experts believe the new highly transmissible variant of the virus has fueled a rising infection rate.

“We are going to be the first country to beat the coronavirus,” Mr. Netanyahu declared in a statement at his office in Jerusalem.

The vow came after days in which health officials warned that Israel’s supply of vaccines was dwindling.

He said planes carrying the vaccine would be arriving soon and boasted that he had spoken to Albert Bourla, Pfizer’s chief executive, 17 times in the past several weeks.

More than 18 percent of Israel’s population has already received the first dose of the vaccine, a rate that has far outstripped the rest of the world and buoyed Mr. Netanyahu’s battered domestic image.

As part of the agreement with Pfizer, Mr. Netanyahu said that Israel would be an “international model for quickly vaccinating an entire country” and that Israeli authorities would share data with the pharmaceutical giant to help “develop strategies to defeat” the virus.

The Israeli health minister, Yuli Edelstein, said the government would give priority to a broader swath of its population to receive the vaccine starting next week. He did not give specifics.

As of Thursday, Israel was permitting people 60 and older to be inoculated, as well as a number of other target groups. It has also provided them to members of the broader public under some circumstances.

Despite his optimism about the vaccines, Mr. Netanyahu was adamant that Israelis abide by the lockdown. “It is forbidden to forget for a moment that the pandemic is raging around the world,” he said.

Israel has averaged 6,695 cases per day over the past week, a substantially higher number than the previous seven days, according to a New York Times database.

Amid surging coronavirus cases, the top U.S. testing official on Thursday announced another scale-up in the country’s diagnostic efforts, touting the importance of tests that can run from start to finish outside the lab.

The government will allocate an additional $550 million to community-based testing programs across all 50 states, said Adm. Brett Giroir, the assistant secretary for health. The government will also put $300 million toward 60 million kits for federal distribution to nursing homes and other vulnerable communities.

Dr. Giroir projected that the country’s capacity for non-laboratory testing could more than double by June.

In a video livestream, Dr. Giroir held up three new at-home testing kits, designed by Ellume, Abbott and Lucira Health, that recently received emergency green lights from the Food and Drug Administration. All can deliver results in a matter of minutes after a quick nasal swab, though only Ellume’s product can be purchased without a prescription.

The Abbott and Ellume tests search for bits of coronavirus proteins called antigens. Lucira’s test, like most laboratory-based tests, hunts for genetic material.

Dr. Giroir, who will depart his position on Jan. 19 as part of the transition to the Biden administration, praised the tests as “sophisticated” but cautioned that none were yet in widespread use. Production ramp-ups are in progress, he noted, but might not alter the market for a few months.

Ellume’s test, for example, while it will be sold over the counter in a few weeks, will still be available in only very limited quantities.

Experts have repeatedly cautioned that rapid tests are not as accurate or consistent as tests that route people’s samples through a laboratory, where they are typically processed with a technique called polymerase chain reaction, or P.C.R.

Rapid tests, which can run from start to finish in a matter of minutes, may also falter more often when used on people without symptoms. Even so, they are often used — as a way to frequently screen some populations like nursing home residents and schoolchildren.

But rapid tests typically have cost and convenience on their side — benefits that Dr. Giroir repeatedly underscored in a call with reporters. He noted the slow and bumpy rollout of testing in the United States, where speedy tests results are still a relative rarity.

Dr. Giroir said it was “not yet obvious” whether widespread at-home testing would be successful.

Susan Butler-Wu, a clinical microbiologist at the University of Southern California’s Keck School of Medicine, said at-home testing might streamline the testing process. People who feel sick could test themselves and determine whether they need to isolate or seek treatment in a matter of minutes.

But outsourcing testing to the general public also carries risks.

Incorrect results, for example, could be tougher to catch, interpret and act on when people test themselves at home. False negatives might embolden people to mingle with others, hastening the spread of the virus, while false positives could unnecessarily keep people out of work or school.

And both types of errors could erode public trust in testing.

Dr. Butler-Wu also noted that rapid test results might not make it to the right care providers and to public health officials when collected at home.

If results aren’t properly reported, she said, “you’re flying blind — you don’t know the prevalence in your community.”

The list of states to identify the dangerous new coronavirus variant is growing.

Texas, Connecticut and Pennsylvania confirmed their first cases on Thursday, joining California, Colorado, Georgia, Florida and New York.

Florida has at least 22 confirmed cases, according to the Centers for Disease Control and Prevention. California has reported at least 26.

Experts have warned that the United States is woefully ill-equipped to track the rapidly transmissible variant. Without a robust, national system to identify genetic variations of the coronavirus, states are left on their own to identify the variant.

The Texas Department of Health and Human Services said an adult male resident of Harris County, which includes Houston, with no history of travel tested positive for the coronavirus. Genetic sequencing this week showed that the infection was caused by the variant.

“The fact that this person had no travel history suggests this variant is already circulating in Texas,” Dr. John Hellerstedt, the commissioner of state health services, said in a statement. “It’s not surprising that it showed up here given how rapidly it spreads.”

Dr. Hellerstedt urged Texans to “redouble our commitment” to social distancing and public health measures.

In Connecticut, Gov. Ned Lamont said two individuals between 15 and 25 years old had tested positive for the variant. Both had traveled outside of the state, he said, one to Ireland and the other to New York. Genetic sequencing showed the cases are unrelated.

Pennsylvania also reported that its case was because of international exposure.

Last month, Britain became the first country to identify the new variant, which is now surging there and burdening its hospitals with new cases. Now, the variant has been identified in at least 33 countries, including Britain. Dr. Hans Kluge, the World Health Organization’s regional director for Europe, called the spread of the variant across the continent “an alarming situation.”

“Without increased control to slow its spread, there will be an increased impact on already stressed and pressurized health facilities,” Dr. Kluge said at a briefing on Thursday, warning that the variant may, over time, “replace other circulating lineages” as it has in Britain.

Dr. Kluge urged countries to continue to investigate transmission, increase genetic sequencing and to share data.

The spread of the coronavirus accelerated sharply in U.S. counties where large universities held classes in person last fall, federal health researchers reported on Wednesday.

Incidence rates in those counties rose more than 50 percent in the first three weeks after classes started, compared with the previous three-week period, according to a new study by the Centers for Disease Control and Prevention. By contrast, infection rates declined in counties without large universities or where large universities held classes remotely last fall, the study said.

The findings come as many students who were home for the holidays prepare to return to campus. They will converge on college towns at a time when the virus is surging in many parts of the country, overwhelming hospitals and straining health care services.

At least 3,964 new coronavirus deaths and 255,728 new cases were reported in the United States on Wednesday, according to a New York Times database.

C.D.C. researchers focused on 101 counties with nonprofit universities that enroll 20,000 students or more and where classes started between July 27 and Aug. 28. The researchers defined remote learning as instruction that appeared to minimize in-person class work on campus; the definition allowed for some in-person instruction for lab and studio courses or for small groups with specific needs.

The incidence of new coronavirus cases was generally declining in early August, the researchers said, though rates among adults aged 18 to 22 were on the rise. Infection rates went on falling — by an average of 18 percent — where large universities chose to teach remotely, the researchers found, but the rates shot up where in-person instruction was underway.

The researchers did not take account of whether students were physically present on campus, even if classes were being held remotely, Dr. Lisa Barrios, a member of the C.D.C.’s Covid-19 response team, pointed out. As a result, she said, it was hard to know whether the large decreases in remote-learning counties happened because fewer students were physically present, or because the universities did other things as well, like impose rigorous mask mandates and bans on social gatherings.

The study also compared counties with large universities teaching in person against counties less than 500 miles away with about the same total population but no large university, and found similarly sharp differences in virus incidence: an 80 percent rise in the university counties, versus a drop of nearly 20 percent in the others.

Dr. Barrios urged universities to increase testing when students return to campus and make adequate provisions to isolate and quarantine infected and exposed students. Students and staff members who catch the virus may increase the risks to people off campus, particularly those who are older or have underlying health problems.

“Most universities don’t exist in a bubble,” Dr. Barrios said. “They are integral parts of their communities.”