Gibson pleaded no contest to drunken driving Aug. 17 for a July incident that made international headlines when he spouted a string of anti-Semitic insults at the arresting officer in Malibu, Calif.
On Monday's broadcast of the TV celebrity news program, Caviezel said he "privately" reached out to Gibson after the actor/director's arrest, but he did not in any way agree with his views.
"Mel Gibson is a brilliant ... everyone knows he's a brilliant director, but I don't agree or support his views," Caviezel said. "I would say that my experience working with him is such that I hope things come back around. (But) I can't support his views on that."
Gibson has publicly apologized and called his remarks "the stupid ramblings of a drunkard."
Gibson was fined and sentenced to three years' probation as well as alcohol rehabilitation classes for his guilty plea.