Representative Jim Jordan of Ohio, the hard-right Republican who is the chairman of the Judiciary Committee, was poised on Friday to make another bid for the speakership, toiling to unite a Republican Conference in chaos after deposing one speaker and blocking another in line for the job.
The bid by Mr. Jordan, the co-founder of the ultraconservative House Freedom Caucus and a favorite of former President Donald J. Trump’s, came as House Republicans were in turmoil after a faction of his supporters forced out former Speaker Kevin McCarthy last week and then refused to back the party’s chosen successor, Representative Steve Scalise of Louisiana, for the job.
“When I decided to run before, I waited until the next day,” Mr. Jordan told reporters at the Capitol on Thursday evening. “I will do the same thing right now,” he added.
House Republicans were set to meet on Friday morning to debate rules for choosing a new speaker, less a day after the abrupt withdrawal of Mr. Scalise, their No. 2 leader, from consideration.
Should Mr. Jordan succeed in winning his party’s nod and draw a majority on the House floor, he would be second in line to the presidency, capping a remarkable rise for a rabble-rousing Republican popular with the party’s far-right base, whose combative style and distaste for compromise has tormented past G.O.P. speakers.
It was unclear whether any other contender would emerge to challenge Mr. Jordan. Mr. Scalise had surpassed him during an internal party contest on Wednesday by just 14 votes. But rather than consolidating his narrow base of backers, Mr. Scalise almost immediately began hemorrhaging supporters, as lawmakers from several factions said they did not intend to fall into line behind him.
Mr. Jordan and his supporters hoped to avoid a similar fate and immediately began calling for Republicans to rally around him shortly after Mr. Scalise’s withdrawal.
But mainstream Republicans have concerns about Mr. Jordan. Several said they did not want to reward his supporters, who refused to honor Mr. Scalise’s nomination.
Representative Ann Wagner of Missouri called Mr. Jordan’s candidacy a “nonstarter.” Representative Don Bacon of Nebraska, who represents a district won by President Biden, said lawmakers were worried about caving to the whims of the hard-right members who had refused to back Mr. Scalise.
“The fact is: If you reward bad behavior, you’re going to get more of it,” Mr. Bacon said.
Representative Kelly Armstrong of North Dakota, a supporter of Mr. Jordan’s, acknowledged that there were Republicans who would not support him “because they don’t want to reward that behavior.”
But he argued that Mr. Jordan should not be judged by the behavior of his most ardent backers and warned that winning a majority would be difficult for any Republican.
“I abundantly don’t think anybody has 217,” Mr. Armstrong said.
There was talk of other options. Mr. McCarthy did not rule out a return to the speakership, saying he would “let the conference decide” whether to reinstate him to the job.
And Representative Patrick T. McHenry of North Carolina, who was named the interim speaker after Mr. McCarthy’s removal, was also being talked about as a potential candidate.
Some members, foreseeing a fight that could last for weeks, were also discussing how they might give Mr. McHenry — whose role is primarily to hold an election for a speaker — more power to carry out the chamber’s work until the conflict could be resolved.
“There is a massive recognition in that room that we need to get a speaker, and we need to stay here in Washington until we do. The world is on fire,” said Representative Andy Barr of Kentucky, a supporter of Mr. Scalise’s. “We cannot allow this dysfunction to prevent us from doing the job of the American people. This is not responsible.”
Mr. Barr said he worried the Republican Party was destroying itself in full view of American voters.
“I think members have got to get it through their heads that they’re squandering a majority,” he said.