Lawmakers exiting a closed-door forum said neither Scalise, the House majority leader, nor Jordan, who chairs the Judiciary Committee, will have a clear advantage when Republicans begin to vote for a nominee by secret ballot on Wednesday.
"We've got two good leaders within our party, with good perspectives on where the party needs to go and an understanding and an emphasis on reuniting the party," Representative Mike Garcia told reporters.
But before voting for a candidate on Wednesday, Republicans will have to decide whether to keep internal disagreements behind closed doors by requiring any nominee to win 217 Republican votes, enough to elect the next speaker on the House floor over Democratic opposition. Current rules require only a simple majority.
"The first order of business is figuring out a rules change that works for the conference," said Representative Kat Cammack.
Republicans hold a narrow 221-212 majority in the House.
The narrowly divided caucus raised some worries that neither candidate would be able to win enough support to be elected speaker in the first round of voting.
"We're going to go get this done tomorrow, and the House is going to get back to work," Scalise told reporters after the candidate forum, which ran over two hours.
Scalise and Jordan each pledged to back whichever candidate ultimately emerged as the nominee, lawmakers said.
Republicans' narrow majority in House made it possible for a fraction of their members to force Kevin McCarthy, who was ousted as speaker last week, to endure 15 grueling floor votes to become speaker in January.
"We need to handle this inside the caucus and not go through what we did in January," said Representative Ralph Norman, who opposed McCarthy at the time.
McCarthy on Monday said he would take the job back if asked to by House Republicans, but on Tuesday told reporters, "I asked them please not to nominate me."
It took only eight Republicans to oust McCarthy last week, which could make leading the caucus a challenge for any new speaker. While McCarthy was the first speaker to be ousted in a formal vote, the prior two Republicans to hold the job left under pressure from party hardliners.
FUNDING DEADLINE
Republicans may have to tackle other thorny issues, including how to move forward on government funding for the fiscal year that began Oct. 1 and whether to change the rule that allowed just one lawmaker to call a vote to oust McCarthy. Current government funding expires on Nov. 17.
Jordan, a prominent hardline conservative backed by former President Donald Trump, told Tuesday's forum that he would back a new stopgap measure to fund the government through April to avoid a partial government shutdown, according to Representative Thomas Massie, a Jordan supporter.
Other lawmakers said Scalise also backed a temporary funding measure, but they offered few details.
Scalise appeared to have the support of many veteran and establishment Republicans including party leaders, while Jordan drew endorsements from others including Trump-style populists.
Representative Patrick McHenry, who is standing in as interim speaker, has been seen as a possible fallback candidate if no one else wins enough votes. But McHenry told reporters on Tuesday that he has not spoken to colleagues about running, adding that there are two candidates.
Until a new speaker is chosen, the House cannot take action. That has brought new pressure on Republicans after Israel declared war on Sunday following an attack by Palestinian militant group Hamas that has prompted calls for more U.S. military aid. Some Republicans are hoping to have a new speaker in place as early as Thursday.