SACRAMENTO, Calif. -- Arnold Schwarzenegger says the affair he had with his family's longtime housekeeper was "the stupidest thing" he ever did to then-wife Maria Shriver and caused great pain to her and their four children.

"I think it was the stupidest thing I've done in the whole relationship. It was terrible. I inflicted tremendous pain on Maria and unbelievable pain on the kids," Schwarzenegger said of the affair that led to a son, who is now 14.

The former Republican governor of California made the comments in an interview with "60 Minutes" that is scheduled to air Sunday, as the one-time "Mr. Universe" and Hollywood action star tries to rebrand himself and promote his new autobiography, "Total Recall: My Unbelievably True Life Story." CBS aired excerpts of the interview Friday.

After leaving the governor's office in January 2011, Schwarzenegger, 65, has launched an effort to redeem his reputation in the wake of the embarrassing public revelations about the affair he had with Mildred Baena, a housekeeper who reportedly worked for the family for 20 years. Their son, Joseph, was born just days after Schwarzenegger's youngest child with Shriver.

Baena listed her former husband as the father on the birth certificate and has said she did not know for certain who the father was until the boy began looking more and more like Schwarzenegger.

The "60 Minutes" interview comes a week after Schwarzenegger launched a think-tank at the University of Southern California, the Schwarzenegger Institute for State and Global Policy. He started it in part, he said, because he accomplished only about half of what he set out to do as governor.

Schwarzenegger has also returned to his acting career, appearing most recently in "The Expendables 2" and the forthcoming "The Tomb," co-starring Sylvester Stallone, and "The Last Stand," which opens in January.

Shriver, a member of the politically powerful Kennedy clan, filed for divorce in July. In a separate excerpt of the "60 Minutes" interview released by CBS earlier this week, Schwarzenegger said Shriver has not read his book.

"I think that Maria is, you know, wishing me well in everything I do," Schwarzenegger said.

According to excerpts obtained Friday by The Associated Press in advance of the book's release, Schwarzenegger says Republican political guru Karl Rove predicted that the 2003 California recall election that put the actor in office would never happen.

Schwarzenegger writes that he visited Rove in early 2003, when the strategist was a top White House adviser.

Not only did Rove tell Schwarzenegger that the election would not happen, he introduced the actor to then-national security adviser Condoleezza Rice as his pick to run for California governor in 2006.

Schwarzenegger felt snubbed.

He asks, "How could Rove have been so wrong?"