Conyers is facing numerous allegations of sexual assault and harassment from former female employees.
Conyers, 88, made the announcement in an interview with a Detroit radio station.
He added, "I want you to know that my legacy will continue through my children".
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Ian Conyers told the newspaper that his great-uncle - the longest-serving current U.S. House member - "is not resigning". He is the longest-serving member in the House.
The move comes amid numerous calls, including from Democratic leadership, for Conyers to step down in light of allegations of sexual misconduct and harassment against him.
News of Conyers' departure comes amid a firestorm of sexual misconduct allegations made against other members of Congress, including Sen.
Democratic Rep. Jerrold Nadler of NY said he was saddened by the resignation of his "friend and mentor" but added: "There can be no tolerance for behavior that subjects women to the kind of conduct that has been alleged".
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On Monday, a woman who said she worked for him for more than a decade said he slid his hand up her skirt and rubbed her thighs while she was sitting next to him in the front row of a church.
Grubbs said she saw Conyers stroking the legs and buttocks of other staffers on multiple occasions.
But Conyers, who took his MI seat in 1965 and was a founding member of the Congressional Black Caucus, insisted that his record would not be tarnished by the accusations.
She said that one time, when she was at Conyers' home, he came out of the bathroom naked when he knew she was in the room.
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Conyers said he did not feel as if he was given due process regarding the allegations, but that it doesn't come as a shock to him, having gone through this with others and worked in the area of constitutional issues and due process in particular for many years. He also was accused of harassment by ethics lawyer Melanie Sloan and sexual harassment by former staff member Deanna Maher. We don't condone sexual harassment on any level, ' he said. Republican House Speaker Paul Ryan has also urged Conyers to step down.
One of them, Marion Brown, last week broke a non-disclosure agreement that she signed after receiving a settlement, reported to be $27,000, when she left her job in Conyers's office, saying she "felt compelled" to speak out. "I hope my retirement will be viewed in the larger perspective of my record of service as I enter a new chapter", the statement from Conyers read.
After a 15-year struggle, Conyers succeeded in winning passage of legislation declaring the Rev. Martin Luther King Jr.'s birthday a national holiday.
Conyers became an icon during the civil rights movement.
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