"After careful consideration and in light of the attention drawn by recent allegations made against me", Mr Conyers said in a statement, he is stepping aside on the Judiciary panel "during the investigation of these matters".
The House Committee on Ethics opened an investigation into Conyers on Tuesday following a Buzzfeed report in which a former staffer said he fired her because she would not "succumb to [his] sexual advances". "He has done a great deal to protect women - the Violence Against Women Act", Ms. Pelosi told NBC Sunday morning.
Conyers, 88, of Michigan's 13th Congressional District, said he notified "the Democratic Leader" of his request as allegations that he sexually harassed female staff members are being investigated.
Ms Pelosi declined to say whether Mr Conyers would suffer any immediate penalty over the allegations.
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Trump came out against the measure as president-elect and said that the USA should use its veto power on the U.N. The resolution later passed after the Obama administration said it would not use the veto power.
Conyers said he denies the accusations and "very much" looks forward to "vindicating" himself before the House Ethics Committee, which announced last week that it was opening an investigation into the accusations against Conyers.
He has rejected calls for his resignation and so has the House's top Democrat - for now. "But I have come to believe that my presence as Ranking Member on the Committee would not serve these efforts while the Ethics Committee investigation is pending".
Pelosi earlier Sunday on "Meet the Press" urged "due process". In that lawsuit, Buzfeed reported, the woman also said Conyers' wife, Monica Conyers, accused the woman of wanting to have an affair with her husband.
Pelosi's defense of Conyers came just minutes after she acknowledged there was a "generational change" in the way sexual harassment allegations are treated, and praised women for increasingly confronting harassers.
Rep. Jackie Speier, D-Calif., who sponsored legislation to overhaul the system by which sexual complaints are made and settled on Capitol Hill, said Congress must show a greater commitment to addressing sexual misconduct.