ORLANDO, Fla. -- Tiger Woods acknowledged Wednesday that he let down his family, saying he regrets "those transgressions with all of my heart."
Woods put a statement on his Web site, offering his "profound apology" to his family and friends.
UsWeekly magazine published a cover story that says a cocktail waitress in Los Angeles carried on a 31-month affair with the married Woods, the world's top-ranked golfer.
"I have let my family down and I regret those transgressions with all of my heart," Woods said in the statement. "I have not been true to my values and the behavior my family deserves. I am not without faults and I am far short of perfect. I am dealing with my behavior and personal failings behind closed doors with my family. Those feelings should be shared by us alone."
Woods has been thrust into the world of tabloid news, and he said Wednesday that he doesn't want to be in that spotlight. He was particularly dismayed about speculation that some domestic abuse between he and his wife, Elin Nordegren, was part of his car accident.
Woods crashed his 2009 Cadillac Escalade into a fire hydrant and into a neighbor's tree about 2:35 a.m. Friday.
The Florida Highway Patrol on Tuesday closed its investigation of the accident, citing the golfer for reckless driving and fining him $164. Woods has already paid the fine, according to court records.
As details - and questions - about the accident surfaced, tabloids began reporting about other women in Woods' life.
The cocktail waitress, Jamiee Grubbs, told UsWeekly she had a voice mail of Woods asking her to do him a favor and take her name off of her cell phone, and that his wife might be calling her.
"Although I am a well-known person and have made my career as a professional athlete, I have been dismayed to realize the full extent of what tabloid scrutiny really means," Woods said. "For the last week, my family and I have been hounded to expose intimate details of our personal lives. The stories in particular that physical violence played any role in the car accident were utterly false and malicious. Elin has always done more to support our family and shown more grace than anyone could possibly expect."
In the most critical comment from a fellow PGA player, Jesper Parnevik said he owed Nordegren an apology for introducing her to Woods. She once worked as a nanny for the Parnevik family.
"We probably thought he was a better guy than he is," Parnevik told The Golf Channel from West Palm Beach, where he is in the final stage of PGA Tour qualifying.
Police said Woods' wife told them she smashed out the back window of his Cadillac Escalade SUV with a golf club to help get him out after he struck a fire hydrant and tree.
"I would probably need to apologize to her and hope she uses a driver next time instead of a 3-iron," Parnevik said, adding that he has not spoken to Woods since the accident.
"It's a private thing, of course," the Swede said. "But when you are the guy he is - the world's best athlete - you should think more before you do stuff ... and maybe not 'Just do it,' like Nike says."
The Associated Press contributed to this article.