The decision sets up a battle within the Conyers family for his Detroit-area House seat. Ian Conyers, a Michigan state senator and the grandson of Mr. Conyers’s brother, said he also plans to run for the seat held by his 88-year-old great-uncle.

“His doctor advised him that the rigor of another campaign would be too much for him just in terms of his health,” Ian Conyers said.

The congressman, who took his Michigan seat in the House in 1965, has already stepped aside as the top Democrat on the Judiciary Committee amid swirling allegations of sexual improprieties. He has been facing intense pressure to resign.

Speaker Paul D. Ryan and Representative Nancy Pelosi, the Democratic leader, have each said Mr. Conyers should resign after a woman who settled a sexual harassment claim against him said on television that the congressman 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.

The younger Mr. Conyers said that despite the accusations, he believes Michigan voters will reward his family’s work in politics by electing him.

The congressman “still enjoys healthy support in our district,” Mr. Conyers 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.”

He said he believed his great-uncle should have due process but stopped short of defending him.

“I stand with my uncle in terms of his belief of no specific wrongdoing,” Mr. Conyers said. “However, those things need to have their day in court.”

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The state senator, who has been in office for about a year, said he had planned to run for re-election next year for his current statehouse seat but would give up that race to run for his great-uncle’s seat in Washington.

“I’m absolutely going to file for his seat. The work of our congressional district, where I come out of, has to continue,” he said. “We have got to have someone who has depth and experience but also historical understanding of what it takes to fight this type of evil in Washington.”

The elder Mr. Conyers plans to call into “The Mildred Gaddis Show,” a local radio program, to make the announcement, the younger Mr. Conyers said. His decision comes as several other lawmakers face allegations of inappropriate behavior.

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

Representative Blake Farenthold, Republican of Texas, is also facing pressure after it was revealed last week that he used $84,000 in taxpayer funds to settle a sexual harassment claim with his former communications director, Lauren Greene. She accused him of regularly making comments to gauge her interest in a sexual relationship, including saying he was having “sexual fantasies” about her.

And last week, an Ohio Army veteran became the fifth woman to accuse Senator Al Franken, Democrat of Minnesota, of inappropriate touching. Senior House Democrats have also begun calling for Mr. Franken to resign.

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