"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.
Cavazos' accusation came Tuesday on Facebook. He alleges Spacey "squeez[ed]" him during the Oscar-winner's tenure as artistic director of the Old Vic theater in London.
In a statement, the Old Vic said it was "deeply dismayed" by the allegations made against Spacey during his time as artistic director.
"There are many of us with a 'Kevin Spacey story,'" Cavazos wrote in a post that has been translated from Spanish.