WASHINGTON — The top two leaders of the House on Thursday called on Representative John Conyers Jr., the chamber’s longest-serving lawmaker, to resign from Congress as widening accusations of sexually inappropriate behavior continued to roil Capitol Hill.

Speaker Paul D. Ryan and Representative Nancy Pelosi, the Democratic leader, each told reporters that Mr. Conyers, Democrat of Michigan, should resign after a woman who settled a sexual harassment claim against him said on television that the lawmaker had “violated” her body, repeatedly propositioned her for sex and asked her to touch his genitals.

Additionally, Representative Joe Barton, a Republican and the Texas delegation’s most senior House member, announced in an interview with The Dallas Morning News that he would not seek re-election after sexually suggestive online messages that he sent a constituent came to light.

And an Ohio Army veteran on Thursday became the fifth woman to accuse Senator Al Franken, Democrat of Minnesota, of inappropriate touching. Senior House Democrats began calling for Mr. Franken to resign.