City and state leaders expressed fears Tuesday that the Trump administration may cease reimbursing some of their purchases of masks, gloves and other personal protective equipment, a move they said could tear new holes in their budgets while threatening public health.

The trouble stems from the Federal Emergency Management Agency, which typically provides funds for disaster relief and has played a central role in the coronavirus pandemic. In calls throughout August, FEMA signaled that it may soon seek to rethink the criteria by which it doles out those dollars, troubling local governments, which say they are desperate for easy-to-access federal cash as the contagion continues to spread.

For one thing, FEMA officials have told cities, states and their emergency responders that they may have to turn to other federal programs to cover some of their coronavirus costs, including protective equipment for government employees and disinfection supplies for schools, according to Erica Bornemann, the director of Vermont’s emergency management agency. She said FEMA has considered the policy changes out of a belief that the country is shifting from responding to the pandemic to reopening amid the lingering outbreak.

“It was eligible in the spring, [but] it may not be going forward,” she said.

FEMA has not finalized its plans, and they could still change, some officials warned. In recent days, the agency’s leaders have told lawmakers on Capitol Hill that they are not planning any major policy announcements that may prevent cities and states from obtaining federal dollars for major costs they have already submitted for reimbursement, according to two people familiar with the briefings who spoke on the condition of anonymity.

But the confusion FEMA has created still prompted mayors and governors to go public with their frustrations Tuesday. In a letter to Peter T. Gaynor, the agency’s administrator, seven groups representing state, city and county leaders joined first responders to slam FEMA for a “troubling pattern of shifting costs and responsibilities onto states and localities when they can least afford it.”

“FEMA and the Administration have long maintained that every disaster is federally supported, state managed, and locally executed,” added the groups, which included the National Governors Association, the National League of Cities, the National Association of Counties and the National Emergency Management Association.

“We call on FEMA to keep its current guidance on emergency protective measures, and encourage the Administration to provide clear guidance on eligibility of funding streams from across the federal government,” they said.

The groups also questioned whether FEMA’s reluctance may stem from the fact that the agency is tapping its disaster relief funds to boost out-of-work Americans’ weekly jobless checks, a program that President Trump commissioned by executive action this month. Many critics have warned for weeks that FEMA may not have enough money to respond to the pandemic, handle the onslaught of hurricane season and implement Trump’s directive.

“It is outrageous that the Trump administration would even consider cutting off critical funding for PPE to prop up the president’s narrow and meager unemployment scheme,” said Evan Hollander, communications director for Democrats on the House Appropriations Committee.

FEMA did not respond to multiple requests for comment.

The potential change in FEMA’s approach to coronavirus funding carries great urgency given the massive budget challenges faced by cities, counties and states nationwide. Widespread closures earlier in the pandemic — and sharp declines in commerce that continue to cut into tax revenue — have prompted many local governments to seek billions of dollars in new aid from Washington.

For months, however, their requests for more support have been met with steep resistance on Capitol Hill and at the White House. Republicans led by Trump have opposed additional state and local aid, making the erroneous assertion that only Democratic-run cities and states are in need of it. The dispute has bogged down a fuller range of relief programs that lawmakers hoped to adopt last month in a successor stimulus bill to the $2 trillion Cares Act they approved in March.

The previous package put aside billions of dollars to help local governments prepare for and respond to the pandemic, including costs related to PPE and shoring up schools. Not long before he signed it into law, Trump also issued a formal declaration that the novel coronavirus constituted a national emergency, opening the door for FEMA to provide funds to augment the country’s response.

FEMA indicated at the time that it would reimburse costs incurred to operate emergency response centers, disinfect public facilities and purchase a wide array of supplies for emergency medical care, according to agency documents. More than five months later, however, city and state leaders said they were surprised to learn that FEMA may not reimburse some of those coronavirus expenses going forward.

In Florida, for example, state education officials had figured for months that FEMA would pay for the protective equipment and disinfectants they needed to reopen schools this fall. Instead, Florida had to shift $30 million in other funds to cover the costs of what Eric Hall, the chancellor for the state’s Department of Education, described in a recent webinar as FEMA’s “indecision.”

On Tuesday, groups representing mayors and governors, their cities, states and counties, as well as state legislatures and first responders blasted FEMA for what they similarly saw as a potential about-face in the middle of a public health crisis. To be sure, FEMA has said that other federal money may cover some of these governments’ costs, according to people who have participated in the calls. But the concern among local leaders is that these federal funds are dwindling or in some cases are already obligated, limiting the pool of financial resources.

“Shifting policy guidance in the middle of a pandemic is impractical, causes confusion, and disrupts operations in states and localities,” the groups wrote. “It also imposes significant bureaucratic and administrative burdens on states during the auditing process at a time when state and local resources are critically strained.”