Xavier Becerra, the secretary of health and human services, hinted on Tuesday that the Biden administration may need to ask Congress for more money to fight the coronavirus pandemic, depending on the scope and severity of a potential new wave of infections fueled by the Omicron variant.

During a round-table discussion with reporters that focused heavily on testing, Mr. Becerra noted that while the administration has some flexibility to move money around, of the $50 billion Congress has allocated for testing, about $10 billion is left. President Biden has made expanded testing a centerpiece of the winter pandemic strategy he announced last week.

“Are we going to have more than $10 billion worth of needs and costs on Covid, especially in regards to testing?” Mr. Becerra said. “There’s a strong chance we will, depending on where Omicron takes us.” He added that his department’s experts were trying to make projections to determine whether additional funding would be necessary — before the need becomes urgent.

“The president said we’ve got to stay ahead of this, so we don’t want to be asking Congress for money after we know we need it,” he said.

With the pandemic heading into its third year, and Omicron on the horizon, much of the money that Congress has allocated for coronavirus response has been spent. The $2 trillion CARES Act was signed by former President Donald J. Trump in March 2020, and the $1.9 trillion American Rescue Plan was signed by Mr. Biden in March 2021. Both were aimed at boosting the economy, as well as addressing Americans’ health needs during the crisis.

The rescue plan included $14 billion to speed up vaccine distribution, and $130 billion to help schools reopen safely, among other coronavirus-related provisions. But the plan, and the CARES Act before it, went into effect before the emergence of the Delta variant this summer, which caused hospitalizations and deaths to spike, adding strain to an already overburdened health care system. The Centers for Disease Control and Prevention has been tracking Omicron cases, which have now turned up in more than 20 states. “Even if most infections are mild, a highly transmissible variant could result in enough cases to overwhelm health systems,” agency officials wrote in a report last week.

On Thursday, the Department of Health and Human Services announced it was releasing $9 billion in “provider relief fund” payments to bolster hospitals and other health care providers that have experienced revenue losses because of the pandemic. More than 69,000 providers in all 50 states, plus Washington, D.C., and eight territories, will receive payments.

In September, the department announced that it would spend a total of $25.5 billion on the effort. That includes the $9 billion released on Thursday and $8.5 billion released last week to rural health care providers. The remainder of the funds will be disbursed in 2022.

In announcing his winter strategy last week, Mr. Biden vowed to fight the pandemic with “science and speed.” He said that people who buy at-home rapid coronavirus tests would soon be eligible for reimbursement from their insurers, and that to ensure access for the uninsured, the federal government would distribute 25 million tests to community health centers and rural clinics.

After the announcement, administration officials said people buying the tests would have to request reimbursement, rather than being reimbursed in the pharmacy as when filling prescriptions. Some public health experts and consumer advocates have balked at that. Mr. Becerra said Thursday that his department was still figuring out the particulars. A number of states have been distributing free at-home tests, including Massachusetts, New Hampshire, Maryland, Colorado and Ohio.

Other countries have spent more heavily on rapid testing. In Britain, citizens can use a government website to order free rapid tests for home use. Germany invested hundreds of millions of dollars to create a network of 15,000 rapid testing sites. The United States has instead focused public purchasing on vaccines, and efforts to encourage their uptake.

On Tuesday, Mr. Becerra pledged, “We are going to make sure that the American people have access to tests and they don’t have to pay out of pocket.”

“How that exactly gets done, we work with our team to make it happen,” he added. “We’re hoping that it will be done in a way that is as smooth as possible.”