Proposition 8 amends the state constitution to declare that "only marriage between a man and a woman is valid or recognized in California." It came in reaction to a state Supreme Court ruling that laws prohibiting same-sex marriage violated the state constitution.

In an appearance Sunday on CNN, Schwarzenegger said the state Supreme Court might overturn Proposition 8, the Los Angeles Times reported. He also said it is likely Proposition 8 will have no effect on the estimated 18,000 same-sex marriages already recorded in California.

"It's unfortunate, obviously, but it's not the end," Schwarzenegger told CNN. "I think that we will again maybe undo that, if the court is willing to do that, and then move forward from there and again lead in that area."

The comments seem to represent a change in Schwarzenegger's thinking, the Times said. In the past he has said he believes marriage should be between a man and a woman, but he has also said the matter should be decided by voters or the courts and he opposed Proposition 8.

He told backers of same-sex marriage they "should never give up."

"They should be on it and on it until they get it done," he said.