In the House of Cards star's lengthy statement, he wrote: "I have a lot of respect and admiration for Anthony Rapp as an actor. I am beyond horrified to hear his story. I honestly do not remember the encounter as 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 behavior."
The 58-year-old also wrote, "This story has encouraged me to address other things in my life...I have loved and had romantic encounters with men throughout my life, and I choose now to live as a gay man."
Rapp, who stars in Star Trek: Discovery and is now 46, alleged in a BuzzFeed News story that Spacey, then 26, tried to 'seduce' him when they were both performing on Broadway.
"He was trying to seduce me," Rapp told the publication. "I don't know if I would have used that language. But I was aware that he was trying to get with me sexually."
Minutes after Spacey's statement was released, Rapp took to Twitter to praise the men and women who have spoken out about their sexual harassment experiences.
He did not address Spacey's apology.