WASHINGTON — President Biden on Thursday stepped up his administration’s response to a coronavirus surge driven by the Omicron variant, sending what he said is urgently needed help to overwhelmed hospitals and pledging to provide Americans with free tests and masks as the country enters the pandemic’s third year.

Mr. Biden said he was directing his staff to purchase an additional 500 million tests for distribution to Americans, doubling the government’s previous purchase as his administration scrambles to respond to the highly contagious Omicron.

In addition, the president said he is sending a total of 120 military medical personnel to six states where hospitals have been overrun by cases. And he promised to reveal next week plans to help Americans by providing free, high-quality masks that are better at prevention infection from the virus.

The announcement about additional tests came as Mr. Biden prepared to get an update from the leaders of his Covid response team at the White House on Thursday morning.

“We’ll continue to work with the retailers and online retailers to increase availability,” he said.

But it is unclear when the tests will be available. Mr. Biden announced the first batch of 500 million tests just before Christmas, and the first batch from that announcement will not start being delivered until later this month, according to White House officials. Details about how Americans can request those tests, including a government-run test website, are slated to be unveiled on Friday.

The president did not say when the new batch of 500 million tests will be manufactured and ready for distribution. But he said the at-home tests — along with more than 20,000 testing sites around the country — will help to meet the surging demand as people try to continue work, school and social life despite the rapid spread of the virus.

“We’re on track to roll out a website next week where you can order free test shipped to your home,” he said, adding that people with medical insurance can also soon get reimbursed for the purchase of up to eight tests a month.

Mr. Biden did not provide any details about what he said would be a plan to ensure that Americans have access to high-quality masks. Experts have said that KN95 and N95 masks protect better against Omicron than the more common cloth or surgical masks that many people wear.

The announcement about help for hospitals was the beginning of a deployment of 1,000 service members to help doctors and nurses deal with a surge in Omicron cases, Mr. Biden said.

The president appeared alongside Lloyd J. Austin III, the defense secretary, and Deanne Criswell, the director of the Federal Emergency Management Agency, at the White House to detail the teams heading to hard-hit communities across the country. Mr. Biden said late last month that he would be tapping the military to help hospitals early in January.

The new teams of doctors, nurses and other medical personnel would begin arriving at hospitals in Michigan, New Jersey, New Mexico, New York, Ohio and Rhode Island, the president said, in order to help triage patients arriving at hospitals, allowing short-staffed emergency departments to free up space.

Each of those states has suffered an astronomical rise in known cases, already exceeding the previous nationwide peak per capita reached last winter, according to a New York Times database. As of Wednesday, Rhode Island has almost hit 700 percent of last winter’s peak, while per-capita cases in New York and New Jersey were between four and five times as high as last year’s nationwide peak.

Hospitalizations per capita in five of the six states have already surpassed last winter’s peak; New Mexico is the exception, at 73 percent of that high point. And with deaths, Michigan, New Mexico and Ohio have climbed higher than the peak in recent days, while New Jersey and New York are inching closer to that level.

The deployments are part of the Biden administration’s efforts to tackle the latest surge of Omicron cases, which have reached more than 780,000 a day across the country. The number of Americans hospitalized with Covid-19 has hit a record high of about 142,000.

As research has emerged that Omicron causes less severe disease and vaccines remain protective against the worst outcomes for the vast majority of people, many public health experts have encouraged less focus on case rates and more emphasis on hospitalizations amid record-breaking national spikes. Still, experts worry that the sheer number of cases will burden health care systems already strained by previous surges and grappling with staffing shortages. Even though at least some hospitalized people test positive for the virus incidentally after being admitted for conditions other than Covid-19, experts say incidental infections can still pose significant health risks.

For Mr. Biden, the inability to get control of the pandemic has helped drag down his approval ratings as he enters his second year in office. His aides are intent on publicly communicating their efforts to deal with the virus.

Since Thanksgiving, when Omicron was first discovered in South Africa, the administration has sent over 800 military and emergency personnel to 24 states, tribes and territories, officials said, not counting the personnel Mr. Biden announced on Thursday.

In addition, more than 14,000 National Guard members have been activated in 49 states to help at hospitals with vaccinations, testing and other medical services, officials said. Those deployments have been paid for by the American Rescue Plan, a law that Mr. Biden championed at the beginning of his term.

Officials said there would likely be further deployments of military medical personnel in the days ahead as the country continues to struggle with the pandemic.

Adeel Hassan contributed reporting.