WASHINGTON — President Trump nominated Cameron Hamilton, a former Navy SEAL, to once again serve as administrator of the Federal Emergency Management Agency on Monday, seeking to install the agency’s first permanent leader of his second term.

If confirmed by the Senate, Mr. Hamilton would return to the post from which he was removed last year, days after he told Congress that FEMA should not be eliminated, an idea floated by Mr. Trump and then-Homeland Security Secretary Kristi Noem.

“The president felt it was only right to give the job to the guy who got fired for defending the agency’s existence,” said a senior administration official who requested anonymity to speak plainly. “This time we expect him to do a better job of not doing the job.”

The nomination follows a Trump-appointed task force report released Thursday that called for limiting federal disaster aid to “truly significant events” and returning most responsibility to state and local governments. Officials have quietly dropped earlier talk of abolishing the agency outright, preferring instead to keep the lights on while ensuring it remains mostly ornamental.

Democrats and disaster-response experts immediately objected, citing a post-Hurricane Katrina law requiring the FEMA administrator to possess actual experience leading disaster management. Mr. Hamilton’s résumé includes managing emergency medical technicians on the southern border and supporting State Department counterterrorism teams.

In a brief statement, Hamilton said he was “honored to accept a position whose primary mission will be to explain to governors why they are on their own.”

The task force is expected to issue additional guidance next month on determining which disasters qualify as “truly significant,” with early drafts reportedly excluding any event that does not personally inconvenience a cabinet secretary.