A strong majority of anti-establishment conservatives in the House Freedom Caucus voted on Wednesday night to support Representative Paul D. Ryan of Wisconsin for House speaker, assuring that he will have the votes to secure the post next week and averting a leadership crisis for Republicans.

Mr. Ryan indicated that he was prepared to seize the gavel and try to bring unity to his party, which has been riven over how House leaders exert authority over members. That fight had become so bitter that it forced the resignation of Speaker John A. Boehner and derailed the candidacy of the majority leader, Representative Kevin McCarthy, to replace him.

“I’m grateful for the support of a supermajority of the House Freedom Caucus,” Mr. Ryan said in a statement, referring to the two-thirds vote he received.

The apparent coalescing of support behind Mr. Ryan, 45, comes at a critical moment for Congress, with votes expected to begin as soon as next week over raising the government’s borrowing authority, the first of several pressing fiscal matters.