Speaking on CBS' "Face the Nation," Hoyer, D-Md., said: "Forcing him out will require a process. But this is bizarre, unacceptable behavior."
Echoing Minority Leader Nancy Pelosi, D-Calif., Hoyer said, "I don't see how he can proceed and effectively represent his constituency."
More photos that Weiner took of himself wearing only a towel in the House gym surfaced Sunday, Politico reported. The congressman says he will take a leave of absence but won't quit.
Rep. Paul Ryan, R-Wis., chairman of the Budget Committee, joining Hoyer on "Face the Nation," said: "This is getting beyond ridiculous. ... We have got to get this behind us because it's a distraction. And so, yes, he should resign."
Hoyer said "a judicial process through the Ethics Committee [is] going to take time.
"I really don't know that we have that time. And I would hope that Mr. Weiner would use this opportunity to reflect upon whether or not he can effectively proceed. I don't see how he can, and I hope he would make that judgment."
Notable deaths of 2014 [PHOTOS]
Ex-Navy SEAL probed over bin Laden revelations