Here’s the latest on the speaker selection.

Several Republicans emerged from a closed-door party gathering on Tuesday night saying they were no closer to coalescing behind a nominee, as several factions had become dug in for their candidates. That set the stage for a potentially raucous and drawn-out secret-ballot vote on Wednesday and suggested that the House might continue without a speaker for days as the party worked through its rifts.

Asked the chances of the House selecting a speaker by Wednesday, Representative Thomas Massie, Republican of Kentucky, said, “I’d put it at 2 percent.”

Lawmakers gathered Wednesday morning on Capitol Hill to begin casting votes in a closed-door session.

A week after a far-right faction forced Speaker Kevin McCarthy from his post, fewer than half of House Republicans had publicly announced their support for either of the leading candidates to replace him: Representative Steve Scalise of Louisiana, the party’s second-ranking leader, and Representative Jim Jordan of Ohio, the Judiciary Committee chairman.

And there was a complicating factor: Supporters of Mr. McCarthy were insisting on a vote to reinstate him, an idea the California Republican has flirted with openly, even after he said on Tuesday that he did not intend to be a candidate.

The unsettled situation reflected deep rifts in the G.O.P. that could prolong the race and lead to a drawn-out fight on the House floor. The chamber has been paralyzed since Mr. McCarthy’s ouster, and members were growing worried that it could not act to support Israel after an invasion by the Palestinian group Hamas that has led to more than 1,000 deaths and scores of hostage takings.

Mr. Scalise and Mr. Jordan gave brief remarks to reporters as they left the forum Tuesday night. Mr. Scalise was pressing for Republicans to unite quickly behind him, while Mr. Jordan and his allies have been angling for a potentially more drawn-out contest.

“We’re putting a strong coalition together,” Mr. Scalise said after emerging from the meeting. “We’re going to get this done tomorrow, and the House is going to get back to work.”

Republicans also were debating possible changes to their internal party rules before the vote, including one that would make it more difficult to kick out a sitting speaker, and another requiring a near-unanimous vote among members of the party before nominating a candidate for speaker.

Both were attempts to avoid a repeat of the embarrassing story arc of Mr. McCarthy’s tenure, in which he suffered through 15 floor votes to gain the speakership in January, then lasted only nine months in the job before he was kicked out by his own party.

Allies of Mr. McCarthy and Mr. Jordan have been pressing to raise the threshold a candidate for speaker would have to reach to be nominated, which could make it more difficult for Mr. Scalise to win the nod. Current party rules require a simple majority of the party’s members, 111 votes, to be nominated; Mr. Jordan and his allies want to require a majority of the House, 218 votes.