The Trump administration confirmed Wednesday that the government will devote an unspecified amount of federal aid to help hospitals cope with the expense of treating covid-19 patients who are uninsured.

Health and Human Services Secretary Alex Azar announced the payments for patients without health coverage as part of several strands of funding the government will distribute from a federal relief package to hospitals and other health-care facilities and practitioners overwhelmed financially by the coronavirus pandemic.

On top of $30 billion already handed out from a $100 billion fund, Azar said $20 billion will soon be disbursed to a broader range of facilities, such as children’s hospitals, that were left out of the first batch.

He said officials are still working on a formula to allot an additional $10 billion to hospitals in communities hit especially hard by covid-19, the illness caused by the novel virus.

Another $10 billion will be devoted to hospitals and clinics in rural areas, where health-care facilities tend to be financially fragile, while $400 million will be given to Indian Health Service facilities, the secretary said.

“The health-care providers on the front lines of the pandemic are heroic,” said Azar, the administration’s most senior health official. “We will continue using every regulatory and payment” tool HHS possesses to help them do “their vital work until we’ve defeated this virus.”

During a conference call with journalists, Azar declined to specify how much money would be allotted to help hospitals with covid-19 cases known as uncompensated care — patients for whom there is no one to pay the bills.

“We are not providing an estimate of that money,” Azar said. He asserted there is “more than sufficient” money to help with the expense of uninsured patients. The amounts he specified add up to slightly more than $70 billion of the $100 billion, but he did not give figures for a few other pots in that fund: money potentially needed for future coronavirus hot spots and covid-19 relief aid for nursing homes, dentists, and doctors and others whose only insurance payments come through Medicaid.

According to Thomas J. Engels, administrator of HHS’s Health Resources and Services Administration, hospitals and other facilities can ask to be reimbursed for treating uninsured covid-19 patients back to Feb. 4.

The government will pay them the same rates as under Medicare, the vast federal insurance program for older Americans.

Those rates are typically less than the reimbursements hospitals receive from private insurance companies. To be eligible for the new payments, Azar said, hospitals and other facilities must promise not to send bills to uninsured patients for any gap between their usual charges and the federal rates.

Without a public dollar amount, it is unclear how much the government’s payments for the uninsured will fill the financial hole covid-19 patients are creating.

The only public analysis of the likely costs, issued this month by the Kaiser Family Foundation, a health policy group, predicted expenses for uninsured patients could be nearly $14 billion to nearly $42 billion over the course of the pandemic.

That range is based on estimates of the number of Americans who get the virus, the rate of infected people who need to be hospitalized and the intensity of the care they need. Kaiser’s analysis included hospitals only — not other parts of the health-care system.

Larry Levitt, Kaiser’s executive vice president and an author of the analysis said, “It would not be surprising if the administration is being coy about some of these amounts, because . . . there is legitimately a massive amount of uncertainty.”

But Levitt added, “If we knew how much the administration was projecting for treatment of the uninsured, we would have a very good sense of how many people they expect to become uninsured in the economic crisis, and how many will get infected. I can certainly imagine why the administration would not want to be specific about their projections.”

Wednesday’s announcement is the second round of explanation by federal health officials of how they are dividing the $100 billion from the Cares Act, a coronavirus relief package that Congress adopted last month. An additional relief measure, approved Tuesday by the Senate and awaiting a final House vote Thursday, would provide $75 billion more to help shore up health-care facilities.

Hospital industry leaders have been eager for federal relief from twin financial pressures caused by the pandemic — the exorbitant cost of caring for the sickest covid-19 patients and the loss of income from having stopped elective surgeries and other types of moneymaking care.

The industry’s main trade groups have urged White House and HHS officials, however, to avoid diverting any of the $100 billion to payments for treating the uninsured, asking them to find other sources of money instead.

Azar’s announcement Wednesday comes nearly three weeks after Vice President Pence first broached the idea in public.

At an April 3 White House briefing, Pence said President Trump’s coronavirus task force was “working out the details” of a proposal “to use some of the $100 billion that we’re making available to hospitals to compensate the hospitals directly for any coronavirus treatment that they provide to uninsured Americans.”

Pence said then that Trump would announce details the next day. “The president has made it very clear: We don’t want Americans to worry about the cost of getting a test or the cost of getting treatment,” the vice president said.

At that briefing, Azar said, “We’re working to ensure that this funding is distributed in a way that is fast, fair, simple and transparent.”

The White House made that announcement while a variety of health-care consumer advocates had intensified pressure on Trump to pursue ways to expand insurance coverage. Advocates have urged the administration to open HealthCare.gov — the online insurance marketplace, usually open six weeks of the year — for individuals and families who do not have health benefits through a job so they can buy health plans under the Affordable Care Act. Other advocates have been pressing for change in a dozen holdout states that have not expanded Medicaid, the hybrid state-federal insurance system for the poor, as the ACA allows.

Trump has made his disdain for the 2010 health-care law a trademark of his political identity and has resisted calls to take such steps.

This article has been corrected to say that hospitals can ask to be reimbursed for treating uninsured covid-19 patients back to Feb. 4, not Feb. 24.