A panel convened by Trump rejects his idea to abolish FEMA.

A task force formed by President Trump to consider changes to the Federal Emergency Management Agency has recommended that it should not be abolished, according to four people briefed on the matter, a position that conflicts with Mr. Trump’s earlier assertion that the agency should “go away.”

It is unclear whether Kristi Noem, the homeland security secretary, will accept the task force’s suggestions. FEMA is part of the Department of Homeland Security. The deliberations underscore a growing tension within Mr. Trump’s political coalition over the federal role in responding to hurricanes, floods, fires and other disasters across the country that are growing more destructive as the planet warms.

Democrats and Republicans agree that the agency is often slow and inefficient. But Republicans, who control Washington, have come to recognize that FEMA aid is crucial to disaster-struck communities and would be difficult, if not impossible, for state and local governments to replace.

Earlier this year Mr. Trump called for dismantling or drastically scaling down FEMA and shifting responsibility for disaster response to the states, saying governors should handle more emergencies on their own. But in the wake of the July 4 floods that devastated the Texas Hill Country, Mr. Trump said that “some good people” were running the agency. Many of the people appointed by the president to the FEMA task force are Republicans from from red states in the South that are vulnerable to hurricanes and reliant on FEMA aid. They include officials from Florida and Texas, two of the states that receive the most federal disaster assistance.

The task force has presented Ms. Noem with a draft report that calls for reforming but preserving the agency in some form, the four people briefed on the matter said. The final report is now expected by the end of the year. It could ultimately suggest a compromise intended to appease the White House, such as renaming FEMA or eliminating the agency “as it exists today” or “in its current form,” two of the people briefed on the matter said.

The draft report, which the Homeland Security Department declined to release to The New York Times, proposes changes to FEMA that would provide aid to states more quickly, according to the four people briefed on the matter. It also suggests that FEMA should not continue sending money to states a decade or more after a disaster has struck. And it floats the idea of restoring FEMA to a cabinet-level agency that answers directly to the president, as it did before 2003.

Ms. Noem is editing the draft report before presenting it to Mr. Trump and has reduced it to roughly 20 pages from around 100 pages, according to the people briefed on the matter. Ms. McLaughlin said that Ms. Noem, the chairwoman of the task force, had not altered the draft report’s findings.

The deliberations over the document come at a tumultuous time for FEMA. David Richardson resigned on Monday as acting administrator of the agency after just six months on the job. Karen Evans, a senior political appointee at FEMA who earlier this year led an overhaul of the federal Cybersecurity and Infrastructure Security Agency, will take over as acting FEMA administrator on Dec. 1. Ms. Evans, like Mr. Richardson, lacks experience in emergency management, which is a legal requirement to lead FEMA.

Ultimately, while the Trump administration can restructure FEMA without congressional approval, eliminating the agency would require an act of Congress. Yet on Capitol Hill, many Republicans have joined with Democrats to support legislation that would make FEMA a cabinet-level agency and reform its operations to move money more quickly to disaster-struck communities. A House committee voted, 57-3, to advance the measure in September.