Arnold Schwarzenegger, who was running for governor of California, admitted to having “behaved badly” after allegations were made that he used his celebrity status to sexually humiliate women.

The claims were made by six women who had met Schwarzenegger on film sets, in studio offices, and elsewhere since the 1970s, and most recently in 2000.

Two of the women, including British television presenter Anna Richardson, agreed to be named in the report published by the Los Angeles Times.

Three of the women stated that Schwarzenegger had grabbed their breasts, and one claimed he had reached under her skirt and gripped her buttocks.

Another woman said Schwarzenegger tried to take her swimsuit off in a hotel elevator.

A sixth woman claimed that the actor had pulled her onto his lap and asked her about a sexual act.

Three of the women could not be named because they work in the film industry, and “He was the highest-paid actor in the world. I was a peon,” said one.

None of the women had ever brought civil actions against the actor.

Schwarzenegger denied most of the allegations, saying “a lot of the stuff in the story is not true … but I have to say that where there’s smoke there’s fire.”

He also acknowledged that he had sometimes “behaved badly” on film sets, saying, “It is true that I was on rowdy movie sets, and I have done things that were not right which I thought then was playful.”

Schwarzenegger’s campaign denied Anna Richardson’s account of an incident in December 2000 when the actor was promoting The Sixth Day at the Dorchester hotel in London.

According to Richardson, Schwarzenegger asked if her breasts were real, then circled her left nipple with his finger and said, “Yes, they are real.”

The allegations had been circulating as rumors for two weeks, and the report was published on the eve of the election, which was set to take place on October 7.

The paper, which was opposed to the recall of Democratic governor Gray Davis, stated that none of the allegations had been brought to its attention by Schwarzenegger’s rivals.

Friends of the women who made the claims said the women had confided in them about the actor long before his run for governor.

Sean Walsh, Schwarzenegger’s spokesman, suggested that the allegations were politically motivated, saying, “We believe Democrats and others are using this to try to hurt Arnold Schwarzenegger’s campaign.”

“We believe that this is coming so close before the election, something that discourages good, hard-working, decent people from running for office.”

Schwarzenegger had dismissed previous allegations about his treatment of women by saying the incidents took place a long time ago, before he was married – and “a lot of crazy things happened in the 70s.”

One woman claimed that Schwarzenegger had touched her breast in 1980 but did not rape her.

Another woman, a former professional beach volleyball player, said the actor had “grabbed and squeezed” her breast after she turned down his invitation to go to his apartment.

Schwarzenegger promised to be a “champion of women” if elected, receiving cheers from the crowd of around 1,500 supporters.

His supporters outside the convention centre in San Diego did not believe the allegations.

“We don’t believe it,” said Susie Hopper, 53, who works for a supermarket. “He’s not that stupid … He lives the American dream.”

Joni Weber, 48, a database designer, said, “He’s an actor – women will come out of the woodwork. Davis is known for his negative campaigning. It would bother me if it was true, but I don’t believe what I read in the papers.”