House Republicans on Thursday abruptly canceled a vote on a resolution directing President Trump to withdraw U.S. forces from Iran or win approval from Congress to continue the war, after it became clear they lacked the votes to defeat the measure.

The retreat was a striking setback that exposed fractures within the G.O.P. over the conflict at a moment when the party has begun pushing back forcefully on Mr. Trump and his agenda.

It also marked the latest embarrassing blow to Speaker Mike Johnson, who has toiled to defeat efforts to challenge or limit the war in line with the president’s wishes, but is contending with growing wariness within his party as the midterm elections approach and the realities of his minuscule majority.

The decision to shelve the war powers resolution came after Republicans had lost control of the floor during an earlier unrelated vote, with several of their members defecting and several more absent. As the House chamber descended into chaos, leaders wary of risking another public defeat on a far more politically consequential vote abruptly scrapped the Iran war measure.

The move came just days after a similar resolution moved ahead in the Senate, when a handful of G.O.P. defectors broke from the president and opposed the war. That vote indicated an increasing willingness by some members of the president’s party to pressure him to end a conflict that a majority of Americans say is not worth the costs.

Last week, a similar measure failed in the House by the barest of margins — on a tie vote — leaving Republican leaders no room for more defections.

“They probably did it because they didn’t have the votes,” said Representative Brian Fitzpatrick, a Pennsylvania Republican who last week sided with Democrats in favor of a similar resolution and said he had planned to do so again on Thursday. “I don’t think they‘re going to have the votes when we get back.”

“The next time they bring it,” he added, “it’s passing.”

It was the fourth time Democrats had sought to challenge Mr. Trump’s ability to wage war without congressional approval since he initiated the current conflict in late February, but with both chambers scheduled for a weeklong recess in observance of Memorial Day, they will have to wait until Congress returns in June.

The delay left Republicans in control of Congress flummoxed and lamenting the dysfunction that has taken hold on Capitol Hill as they struggle to govern.

“All I want is just one normal day,” said Representative Virginia Foxx of North Carolina, who in her role as the chairwoman of the Rules Committee is in charge of controlling proceedings on the House floor. “Just give me one normal day.”