In his first confirmation of using anti-Jewish slurs first reported on the
Internet, Gibson said in a statement that he had no excuses for what he had done.
"There is no excuse, nor should there be any tolerance, for anyone who thinks or expresses any kind of anti-Semitic remark," said Gibson.
His latest apology also came after US gossip magazine, In Touch
Weekly, published photos of Gibson drinking and partying with blonde female fans at Malibu restaurant, Moonshadows, hours before his arrest.
The statement was in contrast to his first apology, released on
Saturday, which while contrite and emotional did not directly mention anti-Semitic remarks he allegedly made to Jewish Los Angeles County sheriff's deputy, James Mee.
Tourists tell
Tourists who were photographed partying with Gibson at Moonshadows just before his arrest said at one point he acknowledged being drunk, but decided to drive home anyway.
Kimberly Lesak, 29, from Louisville, Kentucky, said Gibson late in the night put his head in his hands and acknowledged "I'm drunk".
"We all offered him rides, and he shrugged it off," Ms Lesak told In Touch.
"Mel had bloodshot eyes and looked drunk," Todd Hausberger, 29, of Phoenix, who was also at Moonshadows, told In Touch. "He was slurring his words."
Gibson was urged not to drive the short distance to his Malibu mansion, but Mr Hausberger said Gibson responded: "No, I'm fine. I'll take care of myself."
The Hollywood star has since checked himself into an alcohol rehabilitation program since the Friday dawn incident.
"I want to apologise to everyone in the Jewish community for the vitriolic and harmful words that I said to a law enforcement officer the night I was arrested on a DUI (driving under the influence) charge," he said.
Gibson, 50, who directed of the blockbuster "The Passion of the Christ," has already suffered a blow to his career since asking the arresting officer: "Are you a Jew?" and then blaming Jews for being responsible for all of the world's wars.
Show cancelled
The ABC Television Network cancelled a miniseries about the Holocaust it planned to produce with Gibson's Icon Productions.
The Oscar winning actor-director has come under strong criticism from his peers and the media.
ABC did not refer to the incident in a statement released on Tuesday, saying the decision was made because Gibson had failed to produce a script for the show in time.
"Given that it's been two years and we have yet to see the first draft of the script, we have decided to no longer pursue this project with Icon," ABC said.
A devout, conservative Catholic, Gibson said Tuesday that he was not a "bigot" and that his faith taught him to treat everyone with respect.
"Hatred of any kind goes against my faith," said the star of the "Lethal Weapon" movies and director of “Braveheart”.
"I am not just asking for forgiveness. I would like to take it one step further, and meet with the leaders in the Jewish community, with whom I can have a one-on-one discussion to discern the appropriate path for healing," he said.
Gibson, who was born in American and raised in Australia, was arrested in Malibu, California driving at twice the legal speed limit.
His blood-alcohol level registered one-and-a-half times the limit allowed for drivers under California law.