Rafael Medoff of the US-based David S. Wyman Institute of Holocaust Studies issued the ultimatum after the Walt Disney-owned ABC television said a Gibson company would produce a four-part Holocaust mini-series for the US network next year.
Tentatively titled Flory, the telemovie will tell the true story of Flory Van Beek, a Dutch Jew who survived the Holocaust through the bravery of three Christian families who sheltered her from the Nazis in Holland.
Gibson's Con Artist Productions reportedly clinched the deal with a breathtaking pitch for a climactic "Braveheart-style" battle scene where thousands of Jewish and Nazi combatants rush at each other across an open field.
But Dr Medoff was unimpressed, saying Disney should step in and sack Gibson if he refuses to fully acknowledge the extent of the Nazi genocide.
"By choosing to inject himself into public discussions of the Holocaust by his association with this movie, Mel Gibson has a moral obligation to come clean and clearly repudiate his father's statements denying the Holocaust," Dr Medoff said.
"If he declines to publicly repudiate Holocaust denial and continues to maintain that the Holocaust was just one of numerous similar atrocities during World War II, then Disney and the ABC should reconsider their arrangements with him."
Adding to the controversy is the memory of Gibson's The Passion of the Christ, one of last year's top-grossing films but one condemned as anti-Semitic by many Jewish organisations.
Both the Gibsons were named in the Wyman Institute's 2004 global survey of Holocaust denial.
Hutton Gibson told New York radio station WSNR the Holocaust was mostly fiction because the Nazi's never had enough petrol to burn six million Jews.
"They did not have the gas to do it," he said. "That's why they lost the war." He went on to deny the mass extermination of Poland's Jews, saying they had "simply got up and left".
"They were all over the Bronx and Brooklyn, and Sydney, Australia, and Los Angeles," he said.
When asked last year by ABC reporter Diane Sawyer about his father's statements, Mel Gibson replied: "He's my father. Gotta leave it alone, Diane. Gotta leave it alone."
Asked about his father's religious beliefs and view of the Holocaust in the March 2004 edition of Reader's Digest, Gibson said: "My dad taught me my faith, and I believe what he taught me. The man never lied to me in his life."
Pressed further to go on the record and say the Holocaust happened, Gibson said: "Yes, of course. Atrocities happened. War is horrible. The Second World War killed tens of millions of people. Some of them were Jews in concentration camps. Many people lost their lives. In the Ukraine, several million starved to death between 1932 and 1933."
Dr Medoff said Gibson was trying to "minimise and blur the Holocaust" by making it just one of many atrocities of the war.
"This is ridiculous and clearly contrary to the historical record," he said.
"It indicates that he himself has some sort of distorted, troubling view of the Holocaust."
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