"After careful consideration and in light of the attention drawn by recent allegations made against me, I have notified the Democratic Leader of my request to step aside", said Conyers in a written statement on Sunday.
Nancy Pelosi, the House Democratic leader, said on Sunday that Conyers deserved "due process" as the Ethics Committee inquiry moves ahead, calling him "an icon" who had done much to advance women's causes. BuzzFeed News, which first reported the settlement, said it had received documents from Mike Cernovich, a right-wing commentator.
Conyers, the longest-serving member of the House, had previously said he wouldn't resign and maintained he still has desire to serve but wouldn't allow the charges to "undermine" his colleagues in the Democratic Caucus. "Any credible accusation must be reviewed by the Ethics Committee expeditiously", Ms Pelosi said.
"We are at a watershed moment on this issue, and no matter how great an individual's legacy, it is not a license for harassment", she added. That staffer said she was sacked for rejecting his sexual advances, according to the report.
Conyers is accused of sexually harassing female staff members, and a secret settlement was paid out to one of his accusers.
At least one House Democrat, Rep. Kathleen Rice of NY, has called on Conyers to step down from Congress. "Was it two?" Pelosi asked.
Pelosi earlier Sunday on "Meet the Press" urged "due process".
Pelosi suggested Sunday that the allegations against Franken - including that he kissed a woman against her will - were less serious than those against Moore, who is accused by one woman of sexual advances toward her when she was 14.
Conyers has admitted to making the payment to avoid public litigation, but has denied any sexual harassment claims.
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.