He said he also looked forward to hearing from two other House Republican groups by the end of the week; both are expected to back him.
Republicans are scheduled to vote on nominating a new speaker on Oct. 28, followed by a vote by the full House on Oct. 29.
"The bottom line is if he (Ryan) wants to be speaker, he's got the votes as of tonight," said Representative Mick Mulvaney, a member of the Freedom Caucus who voted for Ryan.
A Ryan spokesman said Ryan was not yet ready to announce his candidacy for speaker because he still had to hear from other Republican groups on whether they would support him.
But those groups' support was expected and that could clear the way for the 2012 Republican vice presidential candidate and current chairman of the House's tax-writing Ways and Means Committee to formally announce by week's end that he is seeking the speakership.
Late on Tuesday, Ryan said he would pursue the top House job if his fellow Republicans united behind him.
Read MoreRyan lays out conditions for seeking speaker's job
The speaker has a major say on legislation that moves through the House and is next in line for the presidency behind the vice president if something were to happen to the president.
Ryan also laid down a series of conditions he wanted to extract from rank-and-file Republicans, including a rules change that would make it more difficult for individual House members to force a vote to oust the speaker.
He spent part of Wednesday meeting privately with the Freedom Caucus and other factions of the 247 Republicans who hold majority control of the House.
The Freedom Caucus issued a statement praising Ryan as a "policy entrepreneur who has developed conservative reforms dealing with a wide variety of subjects." It said he had promised to advance limited government principles and decentralize power to members.
"While no consensus exists among members of the House Freedom Caucus regarding Chairman Ryan's preconditions for serving, we believe that these issues can be resolved within our conference in due time," the statement said.
The Republican Party infighting, which has been on the boil even before Boehner's retirement announcement last month, has overshadowed a stark deadline Congress faces.
If Congress fails to increase the federal government's statutory debt limit by Nov. 3, the Treasury Department has warned of possible catastrophic consequences that could lead to a historic default.
Read MorePaul Ryan would be a great House speaker
A default, which Boehner wants to avoid before he leaves office, could shake financial markets and the economy, but the Republican-controlled Congress had no clear plan yet to prevent it.
For now, the House Republican leadership has not settled on when it would vote to raise the debt limit or what would be in a bill dealing with it. "We're talking a lot about it right now," House Majority Leader Kevin McCarthy told Reuters.
Earlier on Wednesday, the House, in a partisan vote, passed a Republican bill requiring the Treasury to keep borrowing to pay the principal and interest on certain obligations if the debt exceeds the statutory limit.
While the Freedom Caucus is relatively new, having organized early this year, hard line conservatives - many of them small-government Tea Party activists - have had an outsized influence on major fiscal decisions since 2011, when Republicans took control of the House from Democrats.
Since then, the House has repeatedly flirted with a default on Washington's financial obligations. Conservatives forced a 17-day government shutdown in 2013 as they tried to kill the landmark healthcare law known as Obamacare.