Rep. Paul Ryan announced Oct. 20 that he will run for House speaker, saying "this is not a job I ever sought." (C-SPAN)

Rep. Paul Ryan (Wis.) moved closer to the House speakership Tuesday, telling fellow Republicans that he would consider taking the job if he could be assured that the caucus would unite behind him.

Ryan faced his colleagues — and his political future — at a private evening meeting of House Republicans in the Capitol basement. He said he would be willing to step into the speaker’s role, ending weeks of GOP leadership turmoil, as long as disparate factions moved in the coming days to support him.

“I hope it doesn’t sound conditional — but it is,” he said, according to members inside the room. He paused after saying the word “conditional,” they said, for effect.

Ryan, the 45-year-old chairman of the House Ways and Means Committee and a 2012 vice-presidential nominee, has for years resisted pressure to assume a higher-profile role in party leadership. And he signaled Tuesday that his decision to serve was far from final.

Much depends on what assurances of support he can win from Republican hard-liners. Before entering the evening meeting, Ryan met privately with leaders of the House Freedom Caucus, a hard-right group that helped push Speaker John A. Boehner out of his post and derailed Majority Leader Kevin McCarthy’s bid to succeed him.

That meeting ended without specific commitments, according to members present, and at the subsequent GOP conference meeting, Ryan made clear he would need firm support from key groups by week’s end to move forward. The Freedom Caucus was explicitly mentioned, members said, as well as the conservative Republican Study Committee and the moderate Tuesday Group.

In remarks to reporters, Ryan laid out his vision for moving the House GOP “from being an opposition party to being a proposition party” and set terms under which he would assume the speaker’s post. Those terms effectively put the onus on his colleagues to coalesce behind him rather than forcing Ryan to campaign for the job.

“This is not a job I’ve ever wanted, I’ve ever sought,” he said. “I came to the conclusion that this is a very dire moment, not just for Congress, not just for the Republican Party, but for our country.”

Should he agree to assume the speaker’s post, Ryan would once again emerge as a leading force in national politics, three years after serving as his party’s vice-presidential nominee and amid mass unrest in GOP ranks.

“If Paul Ryan can’t unite us, no one can. Who else is out there?” said Rep. Peter T. King (R-N.Y.), a moderate. “That’d be a sign of utter dysfunction, total madness.”

Ryan’s terms reflect a desire to lead the House GOP as its spokesman and agenda setter without the threat of revolt from the right, halting a dynamic that has dominated the tumultuous speakership of Boehner (R-Ohio), who announced last month that he would leave Congress at the end of October.

He told colleagues he would seek to change the rule allowing a simple majority of the House to remove a sitting speaker. The threat of such a vote helped hasten Boehner’s departure.

Rep. Paul Ryan (R-Wis.) is being tapped to become the next speaker of the House, even though he doesn't seem to want the job. Who is this guy? (Gillian Brockell/The Washington Post)

“I laid out . . . what I think it takes to unify this conference, what I think it takes to have a successful speakership, and it’s in their hands,” he told reporters. “I’ll leave it up to my colleagues to decide if I am that unifying person.”

Ryan also said he would delegate much of the job’s travel and fundraising demands if elected so that he could spend enough time with his wife and school-age children: “I cannot and will not give up my family time.”

The terms Ryan set out largely comported with advice he had received publicly and privately from eminent voices inside the Republican Party.

“My only caution is that he should go very slow and make sure that the whole conference is coming to him,” said former House speaker Newt Gingrich (R). “Don’t underestimate the degree of getting chewed up. We are not like the Democrats right now. They are relatively cohesive. . . . We are a movement in enormous ferment, with enormous anger and enormous impatience.”

But looming over Ryan is a churning frustration among Republican activists about the party’s ability to oppose President Obama and a presidential primary field led by anti-establishment outsiders who have made common cause with the House GOP’s right flank.

Those conservative House members have pushed for a suite of rules changes, ranging from an overhaul of the party’s internal steering committee to a more open process for considering legislation. Ryan, they say, would not be exempt from those demands, which, if adopted, could give the new speaker less control.

“The next speaker must follow House rules and commit to an open process for debating and amending legislation,” the Freedom Caucus tweeted shortly before the evening conference meeting began.

Ryan wants House conservatives to make clear that they would not seek to undermine him from the start, said Peter Wehner, a former adviser to President George W. Bush.

“He doesn’t have a moral obligation to get Republicans out of the rubble they’ve created for themselves,” Wehner said. “Asking for their goodwill is completely reasonable.”

Rep. Mick Mulvaney (R-S.C.), a Freedom Caucus member who has expressed measured support for Ryan as speaker, said Ryan could not expect to unify Republicans without making some procedural concessions.

“The displeasure with the way the House has been managed since 2011 is pervasive and crosses all sorts of philosophical boundaries within the party,” Mulvaney said. “The appetite for a new way of doing business is real, and whoever wants to be the speaker is going to have to speak to that.”

Meanwhile, Ryan’s conservative bona fides have been called into question on conservative talk radio and Web sites and in town-hall meetings.

Among his purported apostasies are support for the Troubled Asset Relief Program during the 2008 economic crisis, brokering a spending deal with Democrats in 2013 and — most crucially — being a leading Republican proponent of immigration reform packages that would give illegal immigrants a path to legal status.

Rep. Steve King (R-Iowa), one of the party’s staunchest anti-immigration voices, said the conservative grass roots would have tremendous difficulty trusting Ryan, even if he made clear he had no plans to pursue “amnesty” legislation.

“In the short term, it wouldn’t be a struggle,” he said. “But we know what he believes in. . . . I like him. I respect him. There are big issues that transcend those things, and immigration is one of those.”

A poll released Monday by NBC News and the Wall Street Journal showed strong support for Ryan among Republican primary voters, with 63 percent “comfortable and positive” about Ryan taking over the post. Twenty-eight percent said they would feel “skeptical and uncertain” if he became speaker.

Should Ryan decide not to seek the post, it would set off a free-for-all that has already attracted roughly a dozen potential candidates who have expressed interest in running.

They include powerful committee chairmen such as Homeland Security’s Michael McCaul and Agriculture’s K. Michael Conaway, both of Texas; Jason Chaffetz (Utah) and Darrell Issa (Calif.), respectively the current and former chairmen of the Oversight and Government Reform Committee, as well as up-and-comers such as Marsha Blackburn (Tenn.), who has played a lead role in the GOP’s recent fight against Planned Parenthood.

Most of the members who had floated speaker runs said Tuesday night they would back Ryan. One glaring exception was Rep. Daniel Webster (R-Fla.), who enjoys the endorsement of the House Freedom Caucus — a distinction that can be stripped only if 80 percent of the group’s roughly 40 members vote to do so.

As soon as the meeting broke up Tuesday night, there were signs that the group might chafe at Ryan’s demands.

“There’s still a race for the speakership,” said Rep. Ken Buck (R-Colo.), a Freedom Caucus member. “You don’t hold a conference and have one person talk. I’d like to hear what the other people have to say. I think people could unify behind Paul; I think they could unify behind other people, too.”

Karoun Demirjian, Kelsey Snell and David Weigel contributed to this report.