At least 10 Republicans have announced that they will run for speaker or that they are considering doing so since Friday, when the party cast aside Representative Jim Jordan of Ohio as its latest nominee for the leadership post.

A flood of lawmakers began campaigning just hours after Republicans voted in a closed-door meeting to restart the nomination process after Mr. Jordan, his support ebbing, failed on a third floor vote to win the speakership. The vote essentially ensured that the office of the speaker would remain empty for a third week.

The lawmakers vying for the job include veterans of the House, committee chairmen, a top member of Republican leadership and a sophomore. Virtually none have the kind of commanding national profile normally required of the speaker, who is not only second in line to the presidency but a key fund-raiser for their party’s efforts to protect and expand its majority.

They will have to navigate the same treacherous dynamics of a bitterly divided conference that the three men before them could not, leaving some Republicans openly questioning whether anyone can win a majority of votes on the House floor.

Here are the Republicans who are running — or who are considering running — for speaker.

Mr. Emmer, 62, is the highest-ranking Republican in the race. Endorsed by former Speaker Kevin McCarthy, Mr. Emmer is the No. 3 Republican in the House, whose job is to “whip,” or count votes, to pass the speaker’s agenda.

He is considered among the front-runners, though he could encounter the same issues that dogged Representative Steve Scalise of Louisiana, Republicans’ first failed nominee to replace Mr. McCarthy. Far-right Republican activists have accused Mr. Emmer of being insufficiently supportive of former President Donald J. Trump. And some moderates in the conference were privately unhappy that he did not back an effort to temporarily empower the acting speaker, Representative Patrick T. McHenry of North Carolina.

A former college ice hockey player and coach, Mr. Emmer has allies among both the conservative and the establishment wings of the party.

Mr. Emmer served two terms as the chairman of the National Republican Congressional Committee, helping Republican candidates across the country win elections and making inroads across the conference in the process.

Mr. Scott, 53, was a surprise candidate for the speaker nomination last week, garnering 81 votes in the conference against the better-known Mr. Jordan.

A small-business owner, Mr. Scott was the freshman class president for the 112th Congress.

He is also an ally of Mr. McCarthy and expressed outrage at the Californian’s ouster at the hands of far-right rebels, denouncing them as “nothing more than grifters.”

Mr. Donalds, 44, a member of the ultraconservative House Freedom Caucus, is a favorite of the party’s right wing. This is only his second term in Congress; he won his Naples-based district in 2020.

A native New Yorker, he received as many as 20 votes for speaker on the House floor in January during the prolonged fight that resulted in Mr. McCarthy emerging as speaker.

He has already picked up endorsements from his fellow Floridians.

Mr. Hern, 61, is the chairman of the Republican Study Committee, a group committed to advancing conservative ideology that a majority of the Republican conference belongs to. The post often serves as a springboard to leadership positions. Mr. Jordan and Mr. Scalise, as well as former Vice President Mike Pence, all have led the committee.

Mr. Hern has the conservative credentials that could assuage the hard-right lawmakers who bedeviled Mr. McCarthy, but he is seen as a more moderate option than Mr. Jordan.

Nicknamed the “McCongressman” for his previous ownerships of 18 McDonald’s franchises, Mr. Hern, a former aerospace engineer, was elected to the House in 2018.

Mr. Arrington, 51, rose to prominence this year as the chairman of the Budget Committee, responsible for delivering a framework laying out the spending cuts Republicans said they would demand in exchange for suspending the debt limit.

Mr. Arrington had a pained relationship with Mr. McCarthy as tensions flared around the debt ceiling negotiations. Mr. McCarthy did not trust Mr. Arrington after he floated the idea of supporting Representative Steve Scalise of Louisiana to a colleague midway through Mr. McCarthy’s drawn-out battle for the House speakership in January. Mr. McCarthy later largely cut him out of the negotiations.

A former official in the George W. Bush administration, Mr. Arrington is a favorite of Representative Kay Granger of Texas, the chairwoman of the Appropriations Committee. She could be a powerful ally: Many of the holdouts who sunk Mr. Jordan’s candidacy were veteran members of her panel.

Few people outside of his district may be familiar with Mr. Bergman. A retired Marine Corps lieutenant general, Mr. Bergman, 76, represents Michigan’s Upper Peninsula and the northern half of the Lower Peninsula.

A highly decorated naval aviator, Mr. Bergman has earned cachet with many of the mainstream conservatives — several of whom are military veterans themselves — who opposed Mr. Jordan’s candidacy and want an experienced leader at the helm. Mr. Bergman has presented himself as a temporary option who would work to “steady the ship” and return normalcy to the House.

“What we need right now is a speaker who has experience leading and can put ego aside to work together for the American people,” Mr. Bergman said in a statement. “We need a leader who shuns permanent power and recognizes the current crisis of leadership.”

Mr. Johnson, 51, is a lawyer who is the former chairman of the conservative Republican Study Committee.

An evangelical Christian who is a member of the Judiciary Committee, Mr. Johnson was a key architect of Republicans’ objections to certifying the victory of Joseph R. Biden Jr. on Jan. 6, 2021. Many Republicans in Congress relied on his arguments.

He is an ally and supporter of Mr. Jordan who only considered moving forward with his own bid for speaker after Mr. Jordan fell short.

Mr. Sessions, 68, is the longest-serving member of Congress so far who is considering running for speaker, first serving from 1997 to 2019. After he was defeated in 2018 by a Democrat, Mr. Sessions ran for a seat in a neighboring district and prevailed, returning to Congress in 2021. He has previously served as the chairman of the House Republican campaign committee and as chairman of the powerful Rules committee.

Mr. Sessions participated in a 2019 campaign by Trump allies targeting Marie L. Yovanovitch, the ambassador to Ukraine, writing to Secretary of State Mike Pompeo that she should be fired for repeatedly expressing “disdain” for the Trump administration. (Mr. Trump recalled her in April of that year.)

Mr. Meuser, 59, was elected to Congress in 2018, after serving as his state’s secretary of revenue. He told the National Review that he was considering running for speaker because “I’m not gonna let this kindergarten continue.”