Simmons vehemently denied what he called “these horrific accusations,” saying in a statement emailed to Associated Press that “all of my relations have been consensual”.

The accusations, reported by the New York Times on Wednesday, stem from the 1980s and 1990s. One woman, Drew Dixon, said Simmons raped her in his downtown apartment in 1995. Another, Tina Baker, said Simmons raped her in the early ’90s, when he was her manager. A third, Toni Sallie, a music journalist, said he raped her in 1988, also in his apartment.

Baker was quoted as saying: “I didn’t sing for almost a year.” After the assault, she “went into oblivion”.

Through his lawyer, Simmons told the publication he had “no recollection of ever having any sexual relations with Ms Baker”.

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Sallie dated Simmons briefly in 1987. A year later, Simmons invited her to his Manhattan apartment for a party, she told the New York Times, but when she arrived, she was the only one there, and Simmons led her to his bedroom, pushed her on the bed and raped her. “We were fighting. I said no,” she was quoted as saying. The publication said that Simmons, through his lawyer, acknowledged he had dated Sallie, but denied non-consensual sex.

In each case, the publication said, friends and associates of the accusers said they had been told of the incidents at the time.

It quoted a fourth woman, Christina Moore, who accused Simmons of groping her during a brief encounter in Miami in 2014.

“The current allegations sent to me by the New York Times range from the patently untrue to the frivolous and hurtful. The presumption of innocent until proven guilty must not be replaced by ‘Guilty by Accusation’,” Simmons said in his statement.

He said he would “relentlessly fight against any untruthful character assassination that paints me as a man of violence”.

The allegations weren’t the first to hit the producer and entrepreneur recently. Late last month, HBO said it would edit out any link to Simmons in its All Def Comedy show in the wake of an allegation by screenwriter Jenny Lumet, who said Simmons had sex with her more than two decades ago, despite her repeated demands that he stop.

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Simmons said he had a different memory of the night, but apologised and said he was stepping away from his companies.

Lumet said she went public after model Keri Claussen Khalighi said Simmons coerced her to perform a sex act and later penetrated her without her consent in his New York apartment in 1991. Simmons said the sex with Klalighi was consensual.

Simmons and Rick Rubin founded Def Jam Recordings in 1984. It made stars of such hip-hop artists as LL Cool J, Slick Rick, The Beastie Boys and Public Enemy, and its roster currently includes Kanye West, Justin Bieber, Frank Ocean, Alessia Cara, Jeremih, Jeezy, Iggy Azalea, Big Sean, Nas and 2 Chainz.

— African News Agency