The Trump administration is requiring states to change the way they conduct elections or risk losing tens of millions of federal terrorism-prevention funds, in its latest move that would make voting harder and undermine trust in results that don’t go President Trump’s way.

The effort would force states to transition to paper ballots, verify citizenship of voters and make other changes to election procedures, according to Federal Emergency Management Agency documents.

FEMA, part of the Homeland Security Department, has told states that it would withhold 20 percent of some terrorism-preparedness grants unless they provide “proof of compliance” with the election security measures, the documents show. The grants, which total $1 billion each year, help pay for physical barriers and other security measures as well as planning and drill exercises and cybersecurity protections.

Courts have already blocked similar efforts by the administration to require changes to voting, saying the Constitution grants power over elections to states and not the executive branch.

Mr. Trump and his allies have made false claims of voter fraud for years, which have been investigated and debunked. But since he returned to power last year, he has tried to use the levers of the federal government, along with his influence over state and local lawmakers, to reshape American elections, though with little success. Mr. Trump has pushed new policies through cabinet agencies, including the Justice Department and the Homeland Security Department, and drafted two executive orders seeking to make extensive changes to how elections are run. Both of those executive orders have largely been blocked by courts.

Homeland Security officials said in an unsigned statement that election security and integrity were top administration priorities and that grant recipients should face accountability.

The policies align closely with some of the goals pushed by right-wing activists that are rooted in false conspiracy theories about election machines and voting by noncitizens during the 2020 election.

David Becker, executive director of the Center for Election Innovation and Research in Washington, said he expected the rules to fall if they are challenged in court, adding that they would not increase election security.

“They will actually harm election security,” Mr. Becker said. “These are radical changes to election processes.”

FEMA announced the annual antiterrorism grants on June 24, saying projects to be funded should align with priorities including “protecting the integrity of American elections” and “supporting border security efforts.” A notice warned recipients that 20 percent of any award could be withheld until the Homeland Security Department verifies compliance with the new rules.

The rules do not apply to federal disaster aid, which FEMA also manages.

CNN previously reported on the administration’s plans to tie election security rules to the homeland security grants.

The grants go largely to populous states with large urban areas, including New York, California and Texas. New York is set to receive about $204 million in fiscal year 2026, according to the office of Gov. Kathy Hochul.

“After denying disaster relief funding and stripping millions from counterterrorism programs, the Trump administration is once again putting New Yorkers’ lives at risk to forward their political agenda,” Ms. Hochul, a Democrat, said in a statement about the new requirements. “Unlike the President, my number one priority is New Yorkers’ safety, and I will fight to ensure our state has every resource available to keep us secure.”

The changes could face numerous legal roadblocks, partly because the executive branch does not have constitutional authority to regulate elections, which states administer and Congress broadly oversees.

Last month, a judge barred an effort by the Trump administration to force states to use a centralized national database of citizens built for checking immigration status, known as the SAVE system, to verify voters on their rolls, saying the move violated at least three laws. Two provisions in the FEMA grants would require the same process, according to internal FEMA documents obtained by The New York Times.

The internal documents also show that states would be required to submit plans and timelines to transition from systems that use bar codes or QR codes to rely solely on hand-marked paper ballots. Another provision calls for grant recipients to provide proof that they are conducting manual post-election audits of 5 percent of ballots to ensure electronic systems accurately count votes.

Switching to hand-marked paper ballots would very likely cost states hundreds of millions of dollars, as they would be required to buy new tabulation machines and other election equipment. Hand-marked paper ballots would still require the use of machines to tabulate votes. Nearly every state already has some form of paper ballot backup for audits and tabulation.

Manual audits of 5 percent of ballots would also quite likely to cause significant delays in counting, cost millions of dollars and, in some cases, fall far short of what would be considered an adequate audit for races with narrow margins, as is often the case in some congressional districts and local elections, Mr. Becker said. Currently, every state has a post-election audit process to check for accuracy, according to the National Conference of State Legislators.