A spokesman for the rap impresario said Thursday evening that he "fully supports and will cooperate with the police inquiry and is confident of a swift resolution."
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Simmons, 60, has vehemently denied the allegations, saying in a statement provided to NBC News this week: "These horrific accusations have shocked me to my core and all of my relations have been consensual.
"I have enormous respect for the women's movement worldwide and their struggle for respect, dignity, equality and power," Simmons added.
"I have already apologized for the instances of thoughtlessness in my consensual relations. I have separated myself from my businesses and charities in order to not become a distraction," Simmons said in his statement Wednesday.
In an article published in The Times on Wednesday, three women — former Def Jam executive Drew Dixon, singer Tina Baker and music journalist Toni Sallie — went on the record to accuse Simmons of rape.
The women told The Times they decided to come forward after Hollywood titan Harvey Weinstein was accused of serial sexual harassment and assault over decades, fueling the #MeToo movement and leading to other bombshell claims against powerful men in media and politics.
In a statement given to NBC News, Dixon said: "For the first time in 22 years, I am waking up to a world where the abuse I suffered during my career is finally in my past," adding that she hoped sharing her story would inspire other women in the music industry to come forward.
Tom Winter is a New York-based correspondent covering crime, courts, terrorism and financial fraud on the East Coast for the NBC News Investigative Unit.
Jonathan Dienst is a reporter for WNBC-TV in New York, leading its investigative reporting team and covering justice and law enforcement issues.