In the tweet, he said then-presidential-candidate Donald Trump was "100% correct" that local television news in New York on 9/11 showed Muslims in Jersey City cheering when the towers came down, and he had seen it.
There is no evidence such celebrations occurred.
"I spent my life trying to bring this story of overcoming differences and finding common ground to the screen, and I am incredibly sorry to everyone associated with 'Green Book,'" Vallelonga said in a statement Thursday. "I especially deeply apologize to the brilliant and kind Mahershala Ali, and all members of the Muslim faith, for the hurt I have caused."
He added an apology to his late father Frank Anthony Vallelonga, an actor known professionally as Tony Lip, whose real-life befriending of black concert pianist Don Shirley was the basis for the film. Ali, who is Muslim, plays Shirley and Viggo Mortensen plays the elder Vallelonga.
"'Green Book' is a story about love, acceptance and overcoming barriers, and I will do better," the statement said.
Vallelonga has now deleted his Twitter account.
His old tweet began circulating Wednesday just as "Green Book" director Peter Farrelly was apologizing when a 20-year-old story emerged about him flashing his genitals to colleagues as a joke.
"Green Book" won the Golden Globe on Sunday for best musical or comedy movie.
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