During a backstage interview Monday, Washington denied involvement in a heated on-set incident last year during which an anti-gay slur was reportedly uttered.
"No, I did not call (co-star) T.R. (Knight) a faggot," Washington told reporters. "Never happened, never happened."
On Wednesday, Neil Giuliano, president of the Gay & Lesbian Alliance Against Defamation, said he had contacted Washington's representatives in hopes of meeting the actor to discuss "the destructive impact of these kinds of anti-gay slurs."
"Washington's repeated use of it on-set and in the media is simply inexcusable," Giuliano said in a statement.
Washington's publicist declined comment Wednesday.
Knight, who said soon after the October fracas that he is gay, appeared in Tuesday's taping of "The Ellen DeGeneres Show" to discuss the original incident and Washington's recent comments.
"He referred to me as a faggot. Everyone heard it," Knight said of the October incident.