The two leading candidates to become the next Republican speaker of the House worked the phones and the halls of the Capitol on Thursday, vying for support from within their party’s fractured ranks as the chamber remained in a state of paralysis after the ouster of Representative Kevin McCarthy of California.
Both Representative Steve Scalise, the majority leader, and Representative Jim Jordan, the Judiciary Committee chairman, had landed more than a dozen endorsements by the afternoon as they raced toward a vote of Republicans tentatively scheduled for Tuesday. An election on the House floor could follow the next day, though the process could stretch much longer if no consensus can be reached.
Far from the Capitol, former President Donald J. Trump, whose far-right acolytes in Congress helped lead the rebellion that has plunged the House into chaos, threatened to weigh in himself in what could become an epic struggle.
Mr. Jordan picked up an important G.O.P. backer and cleared a potential challenger from the field with the endorsement of Representative Byron Donalds of Florida, who had previously been exploring his own run for speaker, according to a person familiar with his calls to lawmakers. Mr. Donalds said on the social media site X that Mr. Jordan “has my full support to become the next Speaker of the House!”
Both Mr. Scalise and Mr. Jordan are faced with the difficult challenge of attempting to unite a fractious Republican conference that is reeling after Mr. McCarthy’s removal from the speakership.
For Mr. Jordan, an Ohioan and co-founder of the ultraconservative House Freedom Caucus, the task will be to convince more mainstream Republicans that he can govern and not simply tear things down. He met on Thursday with members of the Main Street Caucus, a group of business-minded Republicans.
For Mr. Scalise, a Louisianian who has won conference elections before as majority leader, the challenge will be to stay one step ahead of Mr. Jordan, and make better inroads with the right wing of the party.
Both men are considered further to the right than Mr. McCarthy, a point Representative Matt Gaetz of Florida, who led the drive to oust Mr. McCarthy, has noted with a sense of satisfaction.
“If it’s Speaker Jim Jordan or Speaker Steve Scalise, there will be very few conservatives in the country who don’t see that as a monumental upgrade over Speaker McCarthy,” Mr. Gaetz said on Newsmax.
Casting a long shadow over race is Mr. Trump, the G.O.P. presidential front-runner who holds heavy sway among congressional Republicans because of his strong standing with the party base, including many of their constituents.
Some right-wing Republicans are encouraging Mr. Trump to make a run for speaker himself, though the party’s current conference rules would block him from doing so because he is under multiple felony indictments and facing the possibility of significant prison time. Even so, Mr. Trump’s allies have floated the idea he might visit the Capitol next week to raise the possibility of a run or otherwise weigh in on the race.
“I’ve been contacted by multiple Members of Congress willing to support and offer nomination speeches for Donald J. Trump to be Speaker of the House,” Representative Troy Nehls of Texas wrote on X. “Next week is going to be HUGE.”
Speaking outside a Manhattan courthouse where is facing a civil fraud case, Mr. Trump seemed to enjoy dangling the possibility, telling reporters: “Lot of people have been calling me about speaker. All I can say is we’ll do whatever is best for the country and for the Republican Party.”
“If I can help them during the process,” he added, “I’ll do it.”
Back in the halls of the Congress, a serious race was taking shape.
Mr. Scalise, who has been in leadership since 2014, has built relationships across the Republican conference. He has been quietly securing commitments through one-on-one calls with members.
On such calls seeking support, Mr. Scalise has emphasized that he is second only to Mr. McCarthy in fund-raising prowess, and he has locked up a string of commitments from the south and the Midwest, according to a person familiar with his private calls, who described them on the condition of anonymity.
“Not only is Steve a principled conservative, he has overcome adversity far beyond the infighting in our conference right now,” said Representative Ashley Hinson of Iowa, who endorsed Mr. Scalise after speaking with him.
One clear point of contrast between Mr. Scalise and Mr. Jordan is their dueling positions on continued aid to Ukraine for its war against Russian aggression, which has become increasingly politicized and is now regarded by many Republicans as toxic.
Mr. Jordan was one of 117 Republicans who voted last week against continuing a program to train and equip Ukrainian troops, while Mr. Scalise sided with 101 Republicans in supporting it.
“Why should we be sending American tax dollars to Ukraine when we don’t even know what the goal is?” Mr. Jordan said Thursday on Fox News. “No one can tell me what the objective is.”
Several Republicans said they were waiting to hear more from the candidates before deciding whom to support.
Representative Marc Molinaro of New York said he had spoken with both Mr. Scalise and Mr. Jordan by phone.
“There really wasn’t any one person in Congress who worked harder to help me get to Congress or to earn my support than Kevin McCarthy,” Mr. Molinaro said.
“We now have individuals who have a week,” he added. “And so I’m going to observe, I’m going to listen, and I’m going to demand that members like me and the people we represent have a seat at the table, and then make a decision.”
Robert Jimison contributed reporting.