In the recording, the Lethal Weapon star chided Eszterhas for reportedly failing to deliver an acceptable first draft of a script for The Maccabees, a now-shelved movie about Jewish hero Judah Maccabee that Gibson had been attached to direct.
Gibson can be heard yelling and screaming on the tape, "Why don't I have a first draft of The Maccabees? What the f**k have you been doing?"
The recording followed a nine-page letter Eszterhas wrote to Gibson, accusing him of anti-Semitism.
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."
Gibson fired back at Eszterhas' claims, branding them "utter fabrications".
"I was very frustrated that when you arrived at my home at the expense of both Warner Brothers and myself you hadn't written a single word of a script or even an outline after 15 months of research, meetings, discussions and the outpouring of my heartfelt vision for this story," wrote Gibson in a letter.
'I've got a little bit of a temper ...'
"Was it just you just swearing at the guy?" Leno asked Gibson of the tape.
"Yeah, pretty much ... maybe you don't know this about me, but I've got a little bit of a temper," Gibson quipped on the show, adding "has it really come to the place where you can't blow off steam in your own home, even if you're justified?"
He continued: "The guy writes a nine-page letter ... if he put half as much time and effort and creativity and imagination into a screenplay, which he was supposed to write, as he did into that letter ... we wouldn't be having this conversation," Gibson added.
"It's kind of like you build a house, you hire a guy to put a roof on it. He comes over and talks about the roof and then you get rained on all night. Wouldn't you be kind of peeved?
"He finally got one, but it was so bad that Warner [Bros] rejected it."
The actor told Leno that the situation has left him "kinda peeved".
"But that's okay," he said. "It's been kinda weird the last couple of years - it's like living in a bad B movie.
"From slipping on a banana peel in your driveway to sort of midnight phone calls ... how did I get here? It is bizarre!"
That's certainly one way of putting it.
Watch Gibson's interview and a trailer for his new movie, Get the Gringo, below:
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