WASHINGTON — Representative Paul D. Ryan said Tuesday that he would be willing to serve as speaker if all the factions of his party could unite behind him, giving hope to House Republicans who have been divided by conflict and confusion.

In what were at times pointed remarks in a private session with his colleagues, Mr. Ryan called for changes both to the way the speaker’s job is structured — focused more on communicating the party’s message and less on fund-raising — and for an end to the antics of “bomb throwers and hand wringers,” according to members in the room.

“We have become the problem,” Mr. Ryan said in a news conference afterward. “If my colleagues entrust me to be the speaker, I want us to become the solution.”

He suggested that he wanted an answer by Friday.

Mr. Ryan made it clear that he would not accede to preconditions set by “one group,” a clear reference to the members of the hard-line Freedom Caucus, which helped push Speaker John A. Boehner into retirement. Now it may be those same hard-liners who are feeling pressure to fall in line behind Mr. Ryan.