Mr. Conyers, however, remained protective of his time in Congress. “I am very proud of the fact that I am the dean of the Congress,” he said on Tuesday. He appreciated the “the incredible, undiminished support” that he had received from his state and the country, he added.

He also did not waver from his stance that he did nothing wrong and called the accusations against him false. “Whatever they are, they are not accurate,” he said. “They are not true. I cannot explain where they came from.”

Mr. Conyers said the allegations were just part of life as a lawmaker.

“This goes with the issue of politics, the game of politics which we are in,” he said. “We take what happens. We deal with it. We pass on and move on forward as we keep going trying to make as much as we can of this tremendous opportunity that has been given to me for so long.”

Mr. Ryan and Ms. Pelosi had each said Mr. Conyers should resign after a woman who settled a sexual harassment claim against him said on television that he had “violated” her body, repeatedly propositioned her for sex and asked her to touch his genitals. Other former staff members have since come forward to say he harassed them or behaved inappropriately.

Ms. Pelosi, in a statement on Tuesday, greeted Mr. Conyers’s announcement unsentimentally.

“Congressman Conyers has served in the Congress for more than five decades and shaped some of the most consequential legislation of the last half-century,” she said. “But no matter how great the legacy, it is no license to harass or discriminate. The brave women who came forward were owed the justice of this announcement.”

Ian Conyers said that despite the accusations, he believed that Michigan voters would reward his family’s work in politics by electing him.

His great-uncle “still enjoys healthy support in our district,” he said.

He added, “People are ready to support our dean and to support our family as we continue to fight, as we have for leading up to a century, for people from Southeast Michigan.”