Gibson appeared Friday on "The Tonight Show with Jay Leno" and discussed the incident that occurred earlier this month with the screenwriter, MSNBC reported.
Eszterhas wrote the screenplay for "Maccabees," about Jewish icon Judah Maccabee, and Gibson is producing.
Gibson said he had been "peeved" because there was a delay in the script. Eszterhas released an audio tape of Gibson yelling at him.
"Was it just you swearing at the guy?" Leno asked about the tape.
"Yeah, pretty much!" Gibson said. "You know, maybe you don't know this about me, but I've got a little bit of a temper."