Days Before a Vote, Republicans Feud Over How to Choose a New Speaker

House Republicans, divided and demoralized after the ouster of their speaker this week, are now quietly feuding over how to elect a successor.

The dispute, which erupted on Friday, suggests that the same divisions that led to the downfall of former Speaker Kevin McCarthy are continuing to fester inside the G.O.P. ranks, setting the stage for a potentially bruising contest next week when lawmakers were set to meet to elect his replacement.

At issue is a request made by more than 90 House Republicans on Friday to temporarily change the party’s internal rules for nominating a candidate for speaker. In a brief letter to Representative Patrick T. McHenry of North Carolina, the interim speaker, and Representative Elise Stefanik of New York, the conference chair, the group requested a “special organizational meeting” to consider the change. The New York Times obtained a copy of the letter.

In the letter, they asked for an amendment to temporarily raise the threshold to become the nominee. Proponents of the change have been pushing to require a unanimous vote of the Republican conference, instead of the current bar of a majority.

They have presented the idea as a way to foster unity after the deeply divisive ouster of Mr. McCarthy at the hands of eight, mostly right-wing rebels who went against the rest of their Republican colleagues this week.

It would, in theory, avoid a replay of the public chaos that unfolded in January, when the nation watched as the House slogged through 15 rounds of roll call votes until Republicans finally coalesced around Mr. McCarthy, a veteran lawmaker from California.

But supporters of Representative Steve Scalise of Louisiana, the majority leader who is running for speaker, quickly cried foul, arguing that the change would only make it more difficult for him to be elected.

The idea that the fractured G.O.P. conference could unanimously come together behind either Mr. Scalise or the other declared candidate, Representative Jim Jordan of Ohio, is also virtually unthinkable.

But Mr. Scalise’s allies believe that he would win a majority over Mr. Jordan, putting him in a strong position to beat the Ohio Republican on the House floor under the current rules.

“Changing the rules is going to create chaos and only advantages candidates who can’t get to 51 percent in the closed-door vote,” said Representative Lance Gooden of Texas, who has said he is backing Mr. Scalise.

Representative Ann Wagner of Missouri, who is also backing Mr. Scalise, said that “a last-minute, rushed rule change is really not what the conference needs right now.”

“We need unity and we need leadership,” she said. “We should all be prepared to support the nominee who the majority chooses.”

She added that there was “nothing binding” about a conference meeting vote. “The only vote that is binding is done in full transparency on the floor of the House of Representatives,” she said.

House Republicans were scheduled to meet behind closed doors on Tuesday to nominate a new candidate for speaker by secret ballot, and a floor vote could take place as early as the next day.

Under the current Republican conference rules, whoever emerges from the secret ballot with a simple majority of votes wins. Changing the rules could lead to a much more drawn-out process wherein both candidates would have to battle to get the entire conference behind them.

Mr. Scalise’s allies regard the effort as a bid by those who are boosting Mr. Jordan’s candidacy to tilt the scales in his favor. One of the people leading the charge for the change was Representative Chip Roy of Texas, who has endorsed Mr. Jordan.

Mr. McCarthy’s allies have also been pressing members to sign on, arguing that the rule change would help keep any infighting behind closed doors. The former speaker has long had a rocky and competitive relationship with Mr. Scalise. And the sense among Mr. Scalise’s backers is that they have a vested interest in helping to elect Mr. Jordan as speaker.

The members who signed the letter come from all factions of the Republican conference. They included Representative Garret Graves of Louisiana, a loyal McCarthy ally, and Representative Bob Good of Virginia, one of the eight hard-right members who voted to oust him.