"Thank you Anthony and all of the others who have risked everything to speak out against sexual assault," the organization added.
"Coming out stories should not be used to deflect from allegations of sexual assault," Sarah Kate Ellis, President and CEO of GLAAD, tweeted.
"This is not a coming out story about Kevin Spacey, but a story of survivorship by Anthony Rapp and all those who bravely speak out against unwanted sexual advances," she added. "The media and public should not gloss over that."
The organization voiced support for Rapp earlier this morning, tweeting, "Thank you Anthony and all of the others who have risked everything to speak out against sexual assault."
Rapp told Buzzfeed in an article published Sunday that Spacey befriended him in the late '80s while they were both performing on Broadway. The actor recalled Spacey inviting him to a party at his apartment, putting him on his bed, climbing on top of him and trying to molest him before Rapp was able to push him off and leave
"I have a lot of respect and admiration for Anthony Rapp as an actor. I'm beyond horrified to hear his story. 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 behavior, and I am sorry for the feelings he describes having carried with him all these years," Spacey said in a statement he released on Twitter Sunday night.
"This story has encouraged me to address other things about my life," the actor continued. "I know that there are stories out there about me and that some have been fueled by the fact that I have been so protective of my privacy. As those closest to me know, in my life 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. I want to deal with this honestly and openly and that starts with examining my own behavior."