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 coronavirus tests for distribution to Americans, doubling the government’s previous purchase as his administration scrambles to respond to the highly contagious Omicron variant.

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.

“That will mean a billion tests in total to meet future demand,” Mr. Biden said. “And we’ll continue to work with the retailers and online retailers to increase availability.”

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 tests 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 the Omicron variant than the more common cloth or surgical masks that many people wear.

“As I’ve said in the last two years, please wear a mask. I think it’s part of your patriotic duty,” he said, acknowledging “it’s not that comfortable, it’s a pain in the neck.”

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.

The deployments are part of the Biden administration’s efforts to tackle the latest surge of cases caused by the highly contagious Omicron variant. As it has surged, so have new cases, reaching 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.

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.

“To the military medical teams on the ground, thank you for all everything you’re doing,” the president said.

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.

Zachary Montague contributed reporting.