Dozens of environmental, labor and health care groups banded together on Monday to file a petition to push the Federal Emergency Management Agency to declare extreme heat and wildfire smoke as “major disasters,” like floods and tornadoes.

The petition is a major push to get the federal government to help states and local communities that are straining under the growing costs of climate change.

If accepted, the petition could unlock FEMA funds to help localities prepare for heat waves and wildfire smoke by building cooling centers or installing air filtration systems in schools. The agency could also help during emergencies by paying for water distribution, health screenings for vulnerable people and increased electricity use.

“Major disaster declarations really open up the broadest pockets of funding that FEMA has available,” said Jean Su, a senior attorney with the Center for Biological Diversity, an environmental group, and the lead author of the petition. “State and local governments are severely ill equipped and underfunded to even deal with emergency measures.”

The support of major labor groups like the A.F.L.-CIO and the Service Employees International Union is part of a broader strategy from unions to create protection for the tens of millions of people working outside or without air-conditioning during heat waves. Unions want the Occupational Safety and Health Administration to require employers to protect workers from extreme temperatures. The White House has pushed officials at the Labor Department, which oversees OSHA, to publish a draft heat regulation this summer. But major business and industry groups, like the U.S. Chamber of Commerce, are opposed to any new requirements.

Labor groups and workers’ rights organizations hope that, if the petition to FEMA is accepted, there would be more pressure for employers to address heat in the workplace.

“If extreme heat and wildfire smoke are designated as major disasters then it’s all hands on deck,” said Christine Bolaños, the communications director of Workers Defense Project, a nonprofit focused on labor rights. A major disaster classification, she said, would force OSHA to make heat worker protections a priority.

The move underscores the growing concerns about the impact of extreme heat among lawmakers, activists and labor groups. Last June, Representative Ruben Gallego of Arizona, a Democrat, introduced legislation to declare extreme heat a major disaster under FEMA’s classification. The bill, which has not progressed, was co-sponsored by 11 Democrats but just one Republican.

Heat already kills more people in the United States each year than hurricanes, floods and tornadoes combined, according to the National Weather Service. Still, the tools to address the consequences of extreme temperatures are being built from scratch.

“None of the world’s institutions, tools, data sets, et cetera are fit for purpose to respond to the size of extreme heat for communities,” said Kathy Baughman McLeod, the chief executive officer of Climate Resilience for All, a nonprofit focused on addressing extreme heat globally.

Over the years, FEMA has denied several similar requests to declare some past heat waves major disasters, including one by California Gov. Gavin Newsom in October 2022, after a record-breaking, triple-digit heat dome formed over the state. At the time, the agency argued that “precedent is to evaluate discrete events and impacts, not seasonal or general atmospheric conditions.”

The 1988 Stafford Act, which authorizes the federal government to declare a disaster or emergency, does not explicitly include extreme heat in its list of 16 causes. But the labor and environmental groups’ petition argues that the agency declared the coronavirus pandemic a major disaster, even though it was also absent from the list, opening a precedent the groups hope to exploit. The petitioners plan to litigate the matter if FEMA again denies the request.

Declaring extreme heat events as major disasters could pose challenges for FEMA. Generally, the agency declares disasters based on how much uninsured public infrastructure was damaged and how many people died. But during heat waves, damaged property is not the main risk, and counting heat-related deaths is difficult, in part because death certificates don’t always reflect the role heat played into a person’s death.

During disasters communities that don’t prepare for extreme events can sometimes receive more funds than communities that do, said Brock Long, who was the administrator of FEMA during the Trump administration.

Mr. Long said he worries that adding new items to the list of FEMA’s major disasters would be like “strapping new parts to a rusty old bicycle frame.”

“It’s time for Congress to sit down with big infrastructure owners and community leaders on how we redesign a system that makes sense,” Mr. Long said. “We are never going to be able to address the changing climate or threats to the future under the existing system.”

If FEMA accepts the petition, it would launch a process to amend its rules to include extreme heat and wildfire smoke as possible major disasters and accept public comment.