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Americans are being advised to steel themselves for one of the most agonizing weeks in living memory, as President Trump and his advisers predicted parts of the country were nearing a peak of cases of covid-19, the disease caused by the novel coronavirus.

The president at Sunday’s White House coronavirus task force briefing hailed numbers from New York showing a one-day decline in deaths while warning of New York and New Jersey, “they’ve really become a very hot zone.”

Still, Trump, along with Vice President Pence, projected confidence not matched by the White House’s medical advisers.

“We’re starting to see light at the end of the tunnel,” Trump said Sunday, even as Anthony S. Fauci, the nation’s top infectious-diseases expert, hedged earlier in the day, saying, “I will not say we have it under control. . . . We are struggling to get it under control.”

Fauci, when asked if dire predictions were at odds with the promise of light at the tunnel’s end, said a peak suggests a possible turning point in the path of the virus but “doesn’t take away from the fact that tomorrow or the next day is going to look really bad.”

The dead in the United States already number more than 9,500, triple the toll of the terrorist attacks that brought the nation low on Sept. 11, 2001. U.S. Surgeon General Jerome M. Adams reached back further to find an analogue for the sense of national alarm, as the country surpassed 333,000 known cases. He said the coming days could bring catastrophe comparable to the attack that drew the United States into World War II in 1941.

“This is going to be the hardest and saddest week of most Americans’ lives, quite frankly,” the surgeon general said in a Sunday appearance on Fox News. “This is going to be our Pearl Harbor moment, our 9/11 moment, only it’s not going to be localized. It’s going to be happening all over the country.”

The virus was transforming life not just here but globally, sending Britain’s prime minister, Boris Johnson, to a hospital Sunday, 10 days after he learned of his positive test. A spokesman for the Conservative Party leader said the hospitalization was a “precautionary step,” as Johnson “continues to have persistent symptoms.”

But the news jolted the United Kingdom, which has recorded more than 48,000 cases and nearly 5,000 deaths, as Queen Elizabeth II, in a rare televised address, urged resolve.

She said the moment recalled her first public speech in 1940, as she addressed children evacuated from their homes because of the war.

“Today, once again, many will feel a painful sense of separation from their loved ones,” she said in a prerecorded video, produced at Windsor Castle.

Trump chose different words but sounded a similar note, predicting “a horrific point in terms of death.” As a treatment for the novel virus, he continued to tout hydroxychloroquine, an antimalarial drug with promising but unproven effects for patients with covid-19, while acknowledging: “What do I know? I’m not a doctor.”

He said the federal government had purchased and stockpiled 29 million doses of the drug, and later blocked Fauci, who heads the National Institute of Allergy and Infectious Diseases, from answering a question about the treatment course. He also said more than 1.6 million tests had been conducted, in a country of about 330 million, and that his administration was gathering equipment “from every corner of Earth” and delivering it across the country.

But places hit hardest by the outbreak continued to report shortages of critical medical equipment, including ventilators, moving states to undertake ad hoc efforts to share the lifesaving breathing devices.

Gov. Jay Inslee (D-Wash.) said Sunday he would return more than 400 ventilators to the national stockpile so they could be used by states facing more dire circumstances, a day after Oregon prepared to dispatch 140 ventilators to New York. Louisiana Gov. John Bel Edwards (D) said he expected the state to exhaust its supply of the machines as soon as Thursday, with ICU beds running out two days later.

Still the worst area of the American outbreak, New York topped 4,000 deaths on Sunday.

The state’s governor, Andrew M. Cuomo, said there were hopeful, though inconclusive, signs. There were fewer fatalities Saturday than Friday, he noted at a briefing in Albany, adding, “You could argue that you’re seeing a slight plateauing in the data, which obviously would be good news.”

Fauci said the measure he was attuned to nationally was the increase in new cases, predicting the death toll would continue to climb even after the country successfully slowed the spread of the outbreak.

“This next week is going to look bad because we’re still not yet at that apex,” he said Sunday on CBS’s “Face the Nation.”

Within about a week, Fauci said, he hoped to “see a flattening out of the curve and coming down,” especially in New York.

Other states were confronting projections that showed critical caseloads arriving as little as a week after the surge battering New York.

In New Jersey, which had more than 37,000 cases as of Sunday, Gov. Phil Murphy (D) said he had secured an additional 500 ventilators. A spokesman for the governor said the allocation from the national stockpile followed three phone calls on Saturday with Pence and Jared Kushner, the president’s son-in-law and senior adviser, as well as Adm. Brett Giroir, the assistant health secretary. The state has received just over half of the 2,500 ventilators it has requested, said the spokesman, Mahen Gunaratna.

In addition to places such as New Jersey and Louisiana, where cases have already surged rapidly, Deborah Birx, the coordinator for the White House’s task force, said over the weekend she was concerned about emerging hot spots in Pennsylvania and Colorado, as well as in Washington, D.C.

At the same time, she said, she was anticipating a “stabilization of cases across these large metro areas where the outbreak began several weeks ago.”

Washington Mayor Muriel E. Bowser (D) on Sunday closed the Wharf’s Fish Market after customers crowded the open-air venue on Saturday, defying the social distancing rules tightened under a stay-at-home order issued late last month. Known cases stood at more than 1,000 in the District.

Pennsylvania, meanwhile, has reported more than 11,500 cases, more than doubling in the four days since Gov. Tom Wolf (D) issued a statewide stay-at-home order.

“This is really scary,” Wolf said in an interview Sunday. He rejected the analogy with warfare, saying an enemy in battle is “something you could actually see.” The other difference, he said, is that ordinary people are on the front lines of the quest to contain the virus, noting that his wife was sewing homemade masks. “We need to buy time,” he said.

States across the country are under directives like Pennsylvania’s. But eight Republican governors have yet to call for all residents to shelter in place. Asa Hutchinson, the governor of Arkansas, said Sunday on NBC’s “Meet the Press” that his “targeted approach” was better.

Trump on Saturday said he would not press governors to take more sweeping measures, even as members of his administration beseeched governors to clamp down. “I just don’t understand why we’re not doing that,” Fauci said on CNN.

Birx said even critical activities should be curtailed if possible, for a while.

“This is the moment to not be going to the grocery store, not going to the pharmacy, but doing everything you can to keep your family and your friends safe,” she said.

The guidance required a painful sacrifice for many Americans, especially those preparing to celebrate religious holidays that mark the onset of spring. Passover, which commemorates struggles for freedom, begins Wednesday night. And Easter, which is Sunday, was the day Trump initially said he hoped to lift federal guidance on restrictions to stem the pandemic because, “That would be a beautiful thing.”

It would have been beautiful, said Solomon Kinloch Jr., the senior pastor of Detroit’s Triumph Church, especially in places such as Michigan, where the virus has exacted a terrible toll on vulnerable populations.

“This process is robbing us of the ability to have authentic relationships,” he said in an interview.

Michigan did not specifically carve out exceptions to its stay-at-home order for religious services, as did other states, though it did stipulate that religious worship in violation of the order would not bring a penalty.

Kinloch said the congregation is doing everything it can to keep its members safe, hosting and streaming “drive-in services” that allow congregants to pull up to a large screen in the parking lot of the church.

“They can even take Communion, if they bring their crackers and juice from home,” he said.

Hannah Natanson and Felicia Sonmez contributed to this report.