© John Nacion/Zuma Press

Confirmed coronavirus cases shot past 1.1 million globally, with the U.S. firmly at the center of the global pandemic and bracing for the country’s hardest weeks.

White House coronavirus coordinator Deborah Birx said during a White House briefing that modeling shows New York, Detroit and New Orleans— and the areas around those cities—will likely reach the peak of their outbreaks in the next six to seven days.

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She declined to predict how many people could perish in those cities, noting that each place is different. But she said that New York has seen several hundred deaths per day and officials there have said that figure could increase into the range of 500-700 people per day.

“That’s very concerning to us,” Dr. Birx said.

Government officials are closely monitoring an uptick in cases in Pennsylvania, Colorado and Washington, D.C., she said, explaining that experts are hopefully social distancing in those places could prevent those areas from seeing the same level of spread as New York, New Jersey, Connecticut and part of Rhode Island are having.

“The next two weeks are extraordinarily important,” she said.

“This is the moment to do everything that you can,” Dr. Birx said later at the briefing, “Doing everything you can to keep your family and your friends safe.”

“There will be a lot of death unfortunately,” President Trump said at the briefing. But he added there would be less death than there would have been without the federal government’s response to stop the spread of the virus.

The U.S. has more than 300,000 cases, and New York state is hardest hit with nearly 114,000 as of Saturday. Upward of 8,100 people in the U.S. have died from Covid-19, the disease caused by the virus, according to Johns Hopkins data. Roughly half of those are in New York, Gov. Andrew Cuomo said.

“It is like a fire spreading,” Mr. Cuomo added on Saturday.

Most states now have stay-at-home orders, with governors in Alabama and Missouri announcing such restrictions Friday.

The Centers for Disease Control and Prevention on Friday evening recommended that all people wear face coverings in public, especially in hot spots with high transmission rates. Officials urged people to reserve surgical masks and N95 respirators for medical first responders and instead encouraged the use of scarfs, bandannas or other cloth coverings. Mr. Trump called the mask advisory “voluntary,” and said he didn’t expect to wear one himself.

Meanwhile in New York City, crematoriums are now running 24 hours a day, and the city put out a wireless emergency alert on Friday asking any licensed medical personnel to volunteer to fight the virus.

Tens of thousands from outside the state had already done so before that call went out, and they and local medical professionals who volunteered are now being paired with hospitals requesting assistance, Mr. Cuomo said.

The governor warned New York is probably about a week away from its caseload apex, when hospitals, health care workers and supplies will be stretched thinnest. The state now has 113,704 cases, up by nearly 11,000 in the past day, Mr. Cuomo said. The death toll rose to 3,565, a one-day jump of 630.

New York state has been struggling to amass enough ventilators, the most in-demand hospital item in the fight against the virus. The Chinese government helped facilitate a donation of 1,000 ventilators, which would arrive on Saturday, Mr. Cuomo said. He also thanked the federal government for its help converting the Javitz Center in Manhattan into a 2,500-bed hospital for Covid-19 patients.

At the White House news briefing Saturday, Mr. Trump said 1,000 medical military personnel were being sent to New York to help with the coronavirus response. He said he had dispatched them and that they would go “where they’re needed the most.”

The president also again criticized many states for asking for too much federal aid, saying that the federal government was there to serve as a “backup” to states.

New Jersey now has more than 34,000 confirmed cases, followed by Michigan, California and Massachusetts. At a news conference Saturday, New Jersey Gov. Phil Murphy said the coronavirus death count now eclipses the death toll from the terrorist attack on 9/11 by more than 100. He asked people to continue to practice social distancing, despite desires to congregate for Easter and Passover in the coming week.

In California, Gov. Gavin Newsom said Saturday the state would increase testing. So far, 126,700 people have been tested, a number that Mr. Newsom said isn’t enough. The state has more than 12,600 confirmed cases, the governor said Saturday.

The state has a new partnership with the University of California, Davis and San Diego, to create a minimum of five to seven testing hubs throughout the state.

“I have a responsibility as governor to do better, and do more testing in the state of California,” Mr. Newsom said at a news conference Saturday.

U.S. medical experts and the White House have estimated the national death toll from the coronavirus pandemic could reach 100,000 to 240,000.

At the same time, governments around the world further tightened limits on social activity, as the death toll surpassed 63,900 world-wide.

In Spain, 124,736 people have tested positive for the coronavirus, according to data updated Saturday morning, more than anywhere else after the U.S. So far, 11,744 people are known to have died there.

But in Italy, long the center of the outbreak, the rate of infection is slowing. There were 119,827 confirmed cases of infection as of Friday evening, a 3.9% increase from the previous day, a sign that the strict social-distancing measures introduced more than three weeks ago are having an impact.

Italy’s official death toll, however, remains the world’s highest, with 14,681 people confirmed dead. But as elsewhere, many people—infected and dead—aren’t being counted.

China, where the new virus first emerged late last year, is slowly returning to normal after lifting one of the world’s longest and most stringent lockdowns. According to Johns Hopkins data, the country has recorded more than 82,500 cases—now surpassed by those in the U.S., Italy, Spain, Germany and France—and the rate of spread has slowed.

President Xi Jinping and other leaders gathered Saturday in Beijing to observe three minutes of silence as part of a national day of mourning for Covid-19 victims.

Write to Melissa Korn at melissa.korn@wsj.com and Newley Purnell at newley.purnell@wsj.com