The "Stranger Things" actress recalled the incident in a weekend (June 21) interview with Britain's Sunday Times newspaper, claiming the "Braveheart" star referred to her as an "oven dodger" at a Hollywood party.
"We were at a crowded party with one of my good friends, and Mel Gibson was smoking a cigar, and we're all talking and he said to my friend, who's gay, 'Oh wait, am I gonna get AIDS?'," Ryder told the newspaper.
"And then something came up about Jews, and he said, 'You're not an oven dodger, are you?'."
While Ryder claimed Gibson tried to apologise to her after the comment, she said she was upset by his words as she had family members who died in the Nazi concentration camps during the Holocaust.
Gibson hit back at Ryder's allegations in a statement via his rep, in which he insisted her account was "100 percent untrue".
And now Ryder has responded once again, sticking to her side of the story and urging the actor to "accept responsibility" for his actions.
"Around 1996, my friend Kevyn Aucoin and I were on the receiving end of his hateful words," she said in the statement via her representative to Access Hollywood. "It is a painful and vivid memory for me. Only by accepting responsibility for our behaviour in this life, can we make amends and truly respect each other, and I wish him well on this lifelong journey."
Ryder's response comes amid reports that Gibson, who upset Jews when comments he made to a Jewish police officer during a drink driving arrest in 2006 went public, will not be asked to reprise his character for the upcoming "Chicken Run 2" sequel.
According to TheWrap, Gibson - who voiced the character of Rocky in the 2000 film - "is not expected to be asked back for the sequel".