The Los Angeles Times newspaper printed a detailed account of alleged sexual misconduct by Mr. Schwarzenegger involving six anonymous women dating back to the 1970s.
According to the Times account, the women came forward on condition they not be identified. They said the bodybuilder turned actor had sexually groped them. The Times says it found out about the allegations on its own and did not receive help from any of Mr. Schwarzenegger's rivals.
On a campaign swing in San Diego, Arnold Schwarzenegger did not specifically address The Los Angeles Times report but he did offer this blanket apology before an enthusiastic crowd of supporters.
"Yes, it is true that I was on rowdy movie sets and I have done things that were not right which I thought then were playful," he said. "But now I recognize that I have offended people and to those people I have offended, I want to say I am deeply sorry about that and I apologize."
It is not clear what impact, if any, the revelations will have on the actor's bid for governor, which has gained ground in recent days.
The target of the recall effort, Democratic Governor Gray Davis, was asked about the story during a campaign appearance near Los Angeles.
"I would just rather leave this matter to the voters of this state," said Mr. Davis. "They will digest it. They will decide the importance to attach to it and they will decide what impact it has on the choices before them next Tuesday."
Several recent polls indicate growing support for the removal of Governor Davis in next week's recall election. Those same polls also indicate that Mr. Schwarzenegger has vaulted into a sizeable lead in the race to succeed Governor Davis should he be recalled by California voters.