Price did not immediately return a request for comment. In Price's absence, Amazon Studios COO Albert Cheng was named interim president, and sources say he is expected to remain in the role has head of the studio.
The controversy may prove to be a setback for Amazon's original video efforts. It's unclear if there will be any other aftershocks for the company.
Price's fiancée, Lila Feinberg, called off their November wedding on Sunday.
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Hackett told THR reporter Kim Masters that she reported the improper behavior to Amazon at the time.
The accusations against Price came in the wake of the Harvey Weinstein scandal that is roiling Hollywood.
The difference last week was that Hackett gave Masters an on-the-record interview with details about the incident. Stories from Weinstein's accusers have brought attention to the long-standing problems of sexual assault and harassment, particularly in Hollywood, and sparked many women to share their own stories using the #MeToo hashtag. Over & over I said it.
Hackett is the daughter of famed science fiction author Philip K. Dick, whose book The Man in the High Castle served as the basis for Amazon's eponymous show.