SAN DIEGO — Faced with new allegations of sexual misconduct, Arnold Schwarzenegger acknowledged on Thursday that "wherever there is smoke there is fire" and apologized for having "behaved badly sometimes" toward women.

Schwarzenegger, who has been surging in the polls in California's recall election, issued the apology here at the beginning of a statewide bus tour. The six-bus tour, with the international media in tow, is part of the actor's final push to replace Gov. Gray Davis.

It was the first time during the extraordinary recall campaign that the actor and former bodybuilder expressed remorse for sexual indiscretions, having previously downplayed allegations of groping and mistreatment of women as exaggerations, mistruths or provocations.

"Yes it is true that I was on rowdy movie sets," Schwarzenegger said, "and I have done things that were not right, which I thought then was playful but now I recognize that I have offended people. And to those people that I have offended I want to say to them, I am deeply sorry about that and I apologize because this is not what I'm trying to do."

The announcement came in response to a front-page Los Angeles Times article Thursday about six women who said that they were the victims of unwanted sexual advances by Schwarzenegger when they came into contact with him on movie sets, studio offices and a gymnasium.

Schwarzenegger's attitude toward women has been an issue since the start of his campaign. But the new allegations — and Schwarzenegger's reply — set off a maelstrom of protest from Schwarzenegger's critics, including women's groups, Democrats, and Arianna Huffington, who dropped out of the race this week but clashed repeatedly with Schwarzenegger during a debate last week.

"I consider his campaign a very expensively produced masquerade, and the question is will the mask be removed before the election or after," Huffington said. "I believe what this story is going to do, is really bring to question this big issue of trust and credibility. If his word and image are consistently proven to be false, he doesn't have a leg to stand on."

According to the Los Angeles Times, three of the women said Schwarzenegger grabbed their breasts. Another said he groped her and tried to strip off her bikini in a hotel elevator. The sixth said Schwarzenegger pulled her to his lap and asked if she was experienced in a particular sexual act.

The allegations covered a 25-year period, ending in 2000.