Spacey initially responded to the allegations through a public statement in October 2017, when he apologised but insisted he didn't have any recollection of the alleged incident.
He said at the time: "I honestly do not remember the encounter, it would have been over 30 years ago.
"But if I did behave then as he describes, I owe him the sincerest apology for what would have been deeply inappropriate drunken behaviour, and I am sorry for the feelings he describes having carried with him all these years."
Spacey also spoke about his own sexual orientation in the statement, having previously been very private about his personal life.
He said: "As those closest to me know, I have had relationships with both men and women. I have loved and had romantic encounters with men throughout my life, and I choose now to live as a gay man."
However, in his recent efforts to have the lawsuit thrown out by a court in New York, Spacey has "categorically" denied the allegations made by Rapp.
He said: "I met [Rapp] several decades ago. I never had a sexual encounter with Mr Rapp. Nor did I harbour any sexual interest or desire in Mr Rapp at that time or any time."
Despite this, a federal judge has set a trial date and Spacey and Rapp are both expected to stand and testify at the hearing.
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