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The announcement came just a week after another man recanted his claims that Clash, 52, had sex with him when he was 16 years old.
"Unfortunately, the controversy surrounding Kevin's personal life has become a distraction that none of us wants, and he has concluded that he can no longer be effective in his job and has resigned from Sesame Street," New York-based Sesame Workshop, the company behind the show, said in a statement.
"This is a sad day for Sesame Street," it added.
In a lawsuit filed on Tuesday, Cecil Singleton is seeking more than $5 million in damages from Clash. Singleton claims he met the then 32-year-old puppeteer in 1993 in a gay chat room when he was 15.
It added that on numerous occasions over a period of years Clash engaged in sexual activity with Singleton.
A representative for Clash was not immediately available for comment on Tuesday.
The unnamed 23-year-old man who first accused Clash recanted his claims last week, saying the relationship was consensual. Clash had denied the allegations and acknowledged a past relationship with his accuser. He added the pair were both consenting adults at the time.
"I am a gay man. I have never been ashamed of this or tried to hide it," Clash said at the time, adding that he was taking a break from the TV show to deal with the situation.
Sesame Workshop said the allegations involving Clash came to its attention in June when the first accuser first contacted the company by email.
The Elmo character debuted on "Sesame Street" in 1979. While Clash was the third performer to animate the child-like shaggy red monster, Sesame Workshop credits him with turning Elmo into the international sensation he became.