WASHINGTON — President Biden accelerated his administration’s coronavirus response on Tuesday as the country faced a surge in cases from a highly contagious new variant, telling anxious Americans that “we should all be concerned about Omicron, but not panicked.”

In a White House address delivered against the backdrop of a new global struggle to cope with the two-year-old pandemic, Mr. Biden said the government will buy a half-billion rapid coronavirus tests and distribute them free to Americans; create new vaccination and testing sites; and send 1,000 military medical professionals to help hospitals nationwide.

“I know you’re tired, really, and I know you’re frustrated,” Mr. Biden said, adding that vaccinated Americans should feel comfortable celebrating with their friends and family for the upcoming holidays. “We all want this to be over, but we’re still in it.”

The president said military troops will begin arriving in Wisconsin and Indiana this week to aid health care workers at hospitals. He said the first of the new testing sites will open in New York within days. And he promised to use the Defense Production Act to help manufacturers better meet the demand for testing.

Mr. Biden acknowledged the political division in the country and the fierce opposition to vaccine requirements among some people, saying his administration has put some mandates in place “not to control your life, but to save your life and the lives of others.” And he pleaded with Americans who remained unvaccinated to get shots to protect themselves and the people around them from infection.

“I honest to God believe it’s your patriotic duty,” Mr. Biden said.

Some of Mr. Biden’s announcements — including the distribution of new at-home tests — are not intended to be implemented for weeks, if not longer, raising doubts about how much they will help in the short term. And most are incremental steps that many public health experts say fall far short of the kind of aggressive actions required.

The president is not moving to mandate testing or vaccination for travelers on domestic flights, and he flatly ruled out on Tuesday returning to the kinds of restrictions that some European nations have once again imposed in an effort to slow the spread of the new variant, which doctors say is even more highly contagious than previous iterations of the virus.

“That’s what I keep getting asked,” Mr. Biden said. “The answer is absolutely no. No.”

Keeping the economy and schools open has been a high priority of the president’s; experts say last year’s school closures were traumatic for many students. Last week, the Centers for Disease Control and Prevention announced a new “test to stay” program, in which students exposed to the virus could take coronavirus tests to remain in the classroom, rather than quarantining at home.

“We know how to keep our kids safe,” Mr. Biden said on Tuesday. “K-12 schools should be open.”

Mr. Biden’s remarks came as officials across the nation, and the world, rushed to confront Omicron in different ways. In New York, Eric Adams, the incoming mayor, postponed his inauguration ceremony. The National Hockey League paused its season ahead of a holiday break, and on Tuesday said its players would not participate in the 2022 Winter Olympics in Beijing. In Massachusetts, state officials called out the National Guard to help staff hospitals with crushing caseloads.

As Europe faced a new virus wave, Germany, Sweden, Portugal and Scotland imposed new restrictions on the movement and activities of their citizens.

Omicron erupted at a precarious moment for the president, who ran on a promise to curb the pandemic, only to be confronted with a shape-shifting virus that is now claiming more than 1,000 American lives every day. It is also a divisive political climate in which many Americans, particularly supporters of former President Donald J. Trump, have refused to get vaccinated.

In his remarks, Mr. Biden acknowledged the former president, noting that Mr. Trump recently said he had received a booster shot, and that “thanks to the prior administration and the scientific community, America is one of the first countries to get the vaccine.”

But he also denounced the “dangerous misinformation on cable TV and social media,” and companies and personalities who were “making money by peddling lies and allowing misinformation that can kill their own customers and their own supporters.”

The president’s moves build on a winter pandemic strategy that he announced three weeks ago, and reflect an awareness inside the White House of the growing threat from the Omicron variant. But Mr. Biden grew defensive in the face of questions about whether he had not moved quickly enough, especially in ensuring that free tests were widely available.

“I don’t think anybody anticipated this was going to spread as rapidly,” Mr. Biden said, rejecting the characterization of his testing response as a failure. He said that over the last few days, “all of a sudden it was like everybody rushed to the counter.”

“It was a big, big rush,” he said.

Just two weeks ago, Jen Psaki, the White House press secretary, mocked the idea of sending a test to every American.

“Should we just send one to every American?” she asked a reporter on Dec. 6. “Then what happens if you, if every American has one test? How much does that cost?”

At least three experts who have been calling for months for the administration to ramp up testing said that the shortfall was entirely predictable, and that the administration’s new testing policy, while a promising first step, was belated.

While Mr. Biden acknowledged that the virus was infecting some vaccinated people, he urged unvaccinated Americans to get their shots, and vaccinated people to get boosters if they are eligible, saying that the unvaccinated have “a significantly higher risk of ending up in the hospital — or even dying.”

Some infectious disease experts say it is simply not possible now to stop the virus from spreading, and that the administration must focus on slowing the spread, protecting the most vulnerable and preventing already strained hospital systems from being overwhelmed.

“The main goal, really, is to prevent people from losing their health and straining hospitals, delaying cancer care and surgeries for people who need it, delaying health care worker burnout,” Dr. Luciana Borio, a former acting chief scientist for the Food and Drug Administration, said in an interview. Preventing infection completely, she said, is “not a winnable battle.”

The Centers for Disease Control and Prevention reported on Monday that Omicron, which was causing less than 1 percent of new Covid-19 cases in the United States as December began, now accounts for nearly three-quarters of new cases. So-called breakthrough infections among vaccinated people are also increasingly common, though many of those cases involve either mild symptoms or none at all.

As a result, experts say, people will have to rely on tests not just to determine whether they are sick, but also to guide them in their daily activities, like going to work or social gatherings. Matching testing supply with demand has been a challenge for both the Trump and the Biden administrations, and the United States has lagged behind Europe in making at-home tests cheap and readily available.

The 500 million tests that the administration intends to purchase, and the website where Americans will be able to request them, will not be available until sometime in January. Much will depend on precisely when that will be.

“It’s fantastic to publicly and clearly acknowledge the important role of testing, but the success now depends on the speed in which these tests can be distributed, and making a clear and easy process to do so,” said Mara Aspinall, an expert in biomedical diagnostics at Arizona State University. “Time is of the absolute essence. January is realistic, but is it Jan. 4 or Jan. 24? There’s a big difference there.”

Some said the testing plan was too little, too late. “A start (finally), but billions are needed to help prevent spread,” Dr. Eric Topol, the founder and director of the Scripps Research Translational Institute, wrote on Twitter. Dr. Topol suggested in a separate essay that the president could have moved more aggressively on other fronts, by distributing KN95 masks to all households, for example.

It was not immediately clear where the tests would come from, how they would be shipped or whether there would be limits on the number an individual could order. Officials said the president would continue to invoke the Defense Production Act to accelerate production of tests.

Mr. Biden’s plan for new federal testing sites will debut in New York City, where several new sites will be running before Christmas. The Federal Emergency Management Agency will also open new pop-up vaccination clinics, officials said, including four in New Mexico that were to open on Tuesday.

Hospital executives said the plan to provide military medical personnel and other workers to beleaguered hospitals should help address some of the severe staffing shortages affecting many facilities.

“It’s a good immediate move,” said Dr. Thomas McGinn, an executive vice president at CommonSpirit, a large Catholic group with 140 hospitals in 21 states, which says its Covid-19 admissions are less than half their former peak.

One of the main challenges hospitals face is the lack of nurses and other workers to handle the expected surge in cases. “There is a staffing shortage in some way shape or form,” said Mark Claster, the former chairman of Northwell Health, the New York hospital chain, and managing partner for Carl Marks Advisors, which provides consulting services to hospitals. “That vacuum needs to be filled, and this is one way to do it.”

But whether the additional workers will be sufficient is far from clear. “We welcome that reinforcement, but we have to understand the gravity of the situation,” said Rick Pollack, the chief executive of the American Hospital Association, a trade group.

As much as the practical problems facing the nation, Mr. Biden tried to address the nation’s battered psyche.

He reminded Americans that despite the Omicron variant, the situation the country is facing today is far different from when the pandemic began in early 2020, when there were no vaccines or treatments and vital medical equipment was in short supply. He insisted, as he has in the past, that there was no need for lockdowns.

“This is not March of 2020,” Mr. Biden declared. “Two hundred million people are vaccinated. We’re prepared; we know more.”

Reed Abelson contributed reporting from Beacon, N.Y.