He also claimed that his former collaborator had continually referred to Jews in front of him as "Hebes," "oven-dodgers" and "Jewboys" while they worked together.
In his letter to Gibson, which was obtained by film industry website The Wrap, Eszterhas said: "I've come to the conclusion that the reason you won't make The Maccabees is the ugliest possible one. You hate Jews."
He continued: "You continually called Jews 'Hebes' and 'oven-dodgers' and 'Jewboys.' It seemed that most times when we discussed someone, you asked 'He's a Hebe, isn't he?' You said most 'gatekeepers' of American companies were 'Hebes' who 'controlled their bosses.'"
He also accused Gibson of having no intention of making the movie.
"I believe you announced the project with great fanfare - 'a Jewish Braveheart' - in an attempt to deflect continuing charges of anti-Semitism which have dogged you, charges which have crippled your career," he wrote.
Gibson hit back at Eszterhas' claims in a letter, branding them "utter fabrications."
"I would have thought that a man of principle, as you purport to be, would have withdrawn from the project regardless of the money if you truly believed me to be the person you describe in your letter," Gibson wrote.
"I guess you only had a problem with me after Warner Brothers rejected your script. Both Warner Brothers and I were extraordinarily disappointed with the draft," he said.
"In 25 years of script development I have never seen a more substandard first draft or a more significant waste of time. The decision not to proceed with you was based on the quality of your script, not on any other factor."
Shortly after the letters were published, Eszterhas claimed that a tape existed which backed up his side of the story.
"He should be very careful calling me a liar," he said last week. "We have a recording of his actions and statements that my son Nick made in Costa Rica."
Eszterhas also said he didn't know what he was going to do with the tape.
However, he has since released the recording, reportedly recorded by his 15-year-old son during a group getaway at Gibson's home in Costa Rica in December.
In the recording, Gibson can be heard yelling at Eszterhas for not having delivered a script yet.
"Why don't I have a first draft of The Maccabees? What the f**k have you been doing?" he screams.
Eszterhas told The Wrap he released the recording because "Gibson called me a liar. And I also have some reason to believe he's creating a PR blitz questioning my truthfulness."
He adds: "The bottom line is it shows to me he badly needs help. My interest isn't to damage him with this tape but to prevent damage being done to others, starting with Jews, including Oksana and now, I'm sure, me.
"I strongly believe that unless he seeks and receives some kind of psychiatric help, someone is going to get hurt."
You can listen to the audio here. (Warning NSFW: Audio and transcript contain very explicit language). Transcript here.
A rep for Gibson says no comment will be issued on the recording beyond his "previously written letter".
But is Gibson angry enough to sue? TMZ reported that the actor is exploring legal action against Eszterhas.
Sources connected with Gibson tell the website that the actor believes he has a "basic human right" not be secretly recorded in his own home.
Gibson's people are also reportedly looking at the laws of Costa Rica "to determine if recording laws were violated," and if the release of the recording violated the actor's privacy rights.
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