Fox, 46, is best known for his work in the TV dramas "Lost" and "Party of Five." He will soon be seen on the big screen in the thriller "Alex Cross."
He was arrested in May for driving under the influence. In a separate incident, a private bus driver accused him in August 2011 of repeatedly punching her while he was drunk because she wouldn't give him a ride to his hotel in Cleveland.
Fox's former "Lost" co-star, Dominic Monaghan, subsequently tweeted a message saying Fox "beats women."
While Fox owned up to the DUI offense, he insisted claims he has been abusive to women are untrue.
The actor told Men's Fitness he "never hit a woman before. Never have, never will."
"I will bet you any amount of money that I will never get behind the wheel of a car after even one drink," he added. "The rest of it, the Cleveland situation, the Monaghan situation -- was a pile of bull[expletive], and I'm not gonna waste too much breath on that."