In claims which were first reported in 2010 by GQ, the 48-year-old actor said Gibson made anti-Semitic and homophobic comments at a party in 1995.
"We were at a crowded party with one of my good friends, and Mel Gibson was smoking a cigar, and we were all talking, and he said to my friend, who's gay, 'Oh wait, am I gonna get AIDS?' And then something came up about Jews, and he said, 'You're not an oven dodger, are you?'" she said.
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Ryder, who personally "had family who died in the [concentration] camps" found the incident "hard" to deal with.
But in a statement released on Wednesday, Gibson's representatives denied the allegations, claiming they are "100 per cent untrue".
"She lied about it over a decade ago, when she talked to the press, and she's lying about it now," the actor's representatives said.
"Also, she lied about him trying to apologise to her back then. He did reach out to her, many years ago, to confront her about her lies, and she refused to address it with him."
Following the statement, Ryder doubled down on the allegations, releasing her own additional statement to Variety.
"I believe in redemption and forgiveness and hope that Mr. Gibson has found a healthy way to deal with his demons, but I am not one of them," she said.
"Around 1996, my friend Kevyn Aucoin and I were on the receiving end of his hateful words. 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."
Gibson, best known for his roles in Mad Max, Braveheart, and Lethal Weapon, has faced a long list of allegations of racism and homophobia in recent decades.