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House Ways and Means Committee Chairman Paul Ryan (R-WI) heads for House Republican caucus meeting in the basement of the U.S. Capitol Oct. 9 in Washington, D.C. Getty Images

U.S. Rep. Paul Ryan, R-Wis., reportedly told House Republicans on Tuesday night that he will seek the job of speaker -- succeeding departing Speaker John Boehner -- if every caucus endorses him, the Hill reported. Immediately after the closed-door meeting, a spokesman for Boehner said Ryan would run only if his colleagues accept him as a “unity candidate” who is backed by House centrists and conservatives.

"Unless the speaker is a unifying figure across the conference, he or she will face the same challenges that have beset our current leadership," said Brendan Buck, a spokesman for Ryan, the Hill reported. “If the members agree with his requests and share his vision, and if he is a unity candidate -- with the endorsement of all the conference’s major caucuses -- then he will serve as speaker. He will be all in," Buck said. "But if he is not a unifying figure for the conference, then he will not run and will be happy to continue serving as chairman of the Ways and Means Committee."

Ryan gave his colleagues until Friday to express their support, the Associated Press reported. “Congressman Ryan has said he's willing to serve if he can get support from the House Freedom Caucus and other groups," said Rep. Darrell Issa, R-Calif.

Tweets circulated online regarding the specifics of what Ryan had said behind closed doors Tuesday night to the GOP House.

Ryan -- who was the running mate of Republican presidential nominee Mitt Romney in 2012 -- had insisted for weeks that he was not interested in the position of speaker. Still, he is a favorite among many Republicans, though he has been criticized by many on the far right on issues such as his 2008 vote to bail out large banks, his longstanding interest in immigration reform and his work on a bipartisan budget measure, the New York Times reported.

“It is tough to bribe a man with no vices or tempt a man with a promotion he doesn’t want,” said U.S. Rep. Tom Cole, R-Okla., a fan of Ryan’s, the New York Times reported. “About all anyone can do is beg and appeal to his sense of duty. There is a lot of that going on.”

Boehner announced last month that he planned to retire from both the speakership and his Ohio congressional seat by the end of October Although he has said that he would not leave before a new speaker is chosen, some House Republicans have suggested they may force him to leave using a procedural move on the House floor.