House Republicans on Thursday narrowly blocked an effort to force an end to the war against Iran and require President Trump to win permission from Congress to continue operations in the Middle East, as the administration continued to defy legal deadlines and a shaky cease-fire dragged on.

The measure was thwarted on a tie of 212 to 212, with a small bloc of Democrats joining nearly all Republicans in voting not to advance it. But the resolution gained some notable G.O.P. backers in the latest sign that the party’s patience for the conflict — and willingness to defer to Mr. Trump on it — is waning.

Representatives Brian Fitzpatrick of Pennsylvania and Tom Barrett of Michigan, both Republicans who are in challenging re-election races and had opposed previous such efforts, broke with their party to support moving ahead with the measure, joining Representative Thomas Massie of Kentucky, who has consistently backed war powers resolutions. Representative Jared Golden of Maine was the lone Democrat to oppose the measure, casting the deciding vote as members of his party pleaded in a chant for “one more” in their ranks to support it just before the speaker gaveled down the vote.

Some Republicans had predicted a broader shift in support within their ranks once the war reached a critical legal deadline of 60 days for the president to seek authorization, which passed on May 1. But the vast majority of the G.O.P. united in backing Mr. Trump, who has declared the conflict terminated and said he does not need approval from Congress to wage war in any case.

The resolution was offered by Representative Josh Gottheimer, Democrat of New York, who early in the conflict had considered voting against it.

But on Thursday, Mr. Gottheimer criticized Mr. Trump’s go-it-alone approach and lack of consultation with Congress.

“I support the administration crushing the Iranian regime. I want to ensure we destroy their nuclear programs, their ballistic missile programs, their drone programs and their terrorist proxy programs,” Mr. Gottheimer said ahead of the vote. “But that said, you cannot leave the United States Congress in the dark any longer. You can’t leave the American people in the darkness.”

“Congress has the authority to authorize the use of force,” Mr. Barrett, one of the three Republicans who crossed party lines to support the Democrat-led measure, said after the vote. “Under the War Powers Act, we’ve delegated some of that to the administration for 60 days. That 60-day point was crossed a couple of weeks ago.”

Most Republicans opposed the measure, which invoked a provision in the 1973 War Powers Resolution that bars a president from using military force without congressional authorization and requires that any such operation wind down after 60 days unless Congress approves.

Many of the president’s most ardent backers pointed to ongoing negotiations and the president’s trip to China as positive signals for a potential breakthrough in the war and warned that a public rebuke would send the wrong message.

“Introducing this provision at this point in time reeks of political gamesmanship when President Trump and his administration are actively engaged in negotiations to bring the tyrannical reign of Iran, the largest state sponsor of terrorism — which the text indicates is the case — to an end,” said Representative Rick Crawford, Republican of Arkansas and the chairman of the Intelligence Committee.

Senior administration officials have argued that the War Powers Resolution is unconstitutional and that, even if it were valid, the deadline would no longer apply because time spent in a cease-fire pauses the clock on the withdrawal deadline. Legal scholars across the ideological spectrum have rejected that view.

But bombing has continued, and on Monday Mr. Trump said the month-old cease-fire was on “life support.”

Democrats’ failure to even force a vote on the measure in the House came a day after a similar effort reached the same fate in the Senate, though more cracks have begun to show in Republican ranks as the party’s patience for the conflict, and Mr. Trump’s handling of it, wears thin.

Democrats have vowed to continue pressing their case against the conflict as economic fallout from the war is felt back in the United States.

Mr. Massie pointed to the pressure of rising costs because of the war as one reason for two of his G.O.P. colleagues to break ranks and vote in support of drawing it to a close.

“It indicates that diesel is six dollars and gas is five, and people can’t afford fertilizer because of this war,” he said in an interview after the vote.

Mr. Trump’s opponents cited his assertion this week that he doesn’t “think about Americans’ financial situation” amid negotiations with Iran as they made the case that the war has harmed U.S. interests.

“Trump’s war with Iran has cost thousands of lives and spiked the price of everything from gas to groceries,” Representative Greg Casar of Texas, the chairman of the Congressional Progressive Caucus, said in a statement. “We will keep holding Republicans in Congress accountable for as long as they enable this reckless, illegal war.”

Megan Mineiro contributed reporting.