By David Morgan and Katharine Jackson

WASHINGTON The U.S. House of Representatives is due to hold a third vote to fill its vacant speaker's chair on Friday, but Republicans who control the chamber appear no closer to resolving a leadership battle that has paralyzed the House for more than two weeks.

Outspoken conservative Jim Jordan, who has twice failed this week to win the job, is expected to make a third attempt when the House opens for business at 10:00 a.m. ET (1400 GMT) on Friday.

His opponents say he is likely to fare worse this time than he has before.

Republican infighting has left Congress unable to act on President Joe Biden's request for aid to Ukraine and Israel.

The narrow and fractious Republican majority has failed to unite behind Jordan or any other candidate to replace Speaker Kevin McCarthy, who was ousted by a handful of party members on Oct. 3. They also have been unable to agree on a fallback plan that would let the chamber take up legislation.

Jordan has failed to win the 217 votes needed to claim the speaker's gavel in votes on Tuesday and Wednesday.

He met privately on Thursday with some of the 22 Republicans who have voted against him.

But the holdouts, some of whom have received death threats, said they were unmoved.

"We all told him that we're solid no's. That was the discussion. Now he's got a decision to make," Republican Representative Vern Buchanan told reporters after the meeting.

Republicans control the House by a 221-212 margin, and Jordan has not gotten more than 200 votes so far.

A third failed vote could prompt Jordan to drop out, which would clear the way for other candidates to emerge. But it is unclear whether Republicans will be able to unite behind any of them.

Republicans also are divided on a backup option that could allow the chamber to address pressing matters, like Biden's aid package and spending legislation that would allow the U.S. government to keep functioning beyond a Nov. 17 deadline.

That plan would give more authority to Republican Representative Patrick McHenry, who is filling the speaker's chair on a temporary basis. House Democrats and the White House have said they are open to the idea, but Republicans rejected that approach in a closed-door meeting on Thursday.

The impasse has exposed sharp divisions between Republicans who aim to work within the rules of Washington politics and a hard-right faction that has taken the U.S. government to the brink of default and the edge of a shutdown.

Investors say the turmoil on Capitol Hill is also contributing to market volatility.

"People are really trying to figure out how they can unite around a body that has really done this self-inflicting wound," said Republican Representative Kat Cammack.

Jordan has built his reputation as a leader of that uncompromising right flank. His backers say that would make him an effective fighter for conservative policies in a town where Democrats control the Senate and the White House.

A close ally of Donald Trump, Jordan was a "significant player" in the former president's attempts to overturn Biden's 2020 election win, according to a congressional investigation. He helped to engineer government shutdowns in 2013 and 2018 and helped to pushed Republican Speaker John Boehner into retirement in 2015.

As chair of the Judiciary Committee, he is a leader of an impeachment inquiry into Biden that has so far turned up no evidence of wrongdoing by the president.

(Reporting by David Morgan, Katharine Jackson and Moira Warburton, writing by Andy Sullivan; Editing by Scott Malone and Grant McCool)