THOUSAND OAKS, Calif. — With a public apology and another appeal for privacy, Tiger Woods acknowledged Wednesday that he let his family down with unspecified “transgressions” that he regrets with “all of my heart.”

“I have not been true to my values and the behavior my family deserves,” Woods said on his Web site following a magazine report of an alleged affair.

It was his longest statement since a middle-of-the-night car crash outside his Florida home last week set off the greatest media scrutiny of Woods’ career and his 5-year-old marriage to former model Elin Nordegren. He did not go into detail and said he would deal with his “personal failings” with his family.

“Those feelings should be shared by us alone,” he said.

Shortly after the investigation of the car accident ended Tuesday with a $164 citation for careless driving, Us Weekly reported that a Los Angeles cocktail waitress claims she had a 31-month affair with the world’s No. 1 golfer.

About three hours before Woods’ statement, the magazine released what it said was a voice mail — provided by the waitress, Jaimee Grubbs — that Woods left on her phone three days before his accident.

“I will strive to be a better person and the husband and father that my family deserves,” Woods said on his Web site. “For all of those who have supported me over the years, I offer my profound apology.”

— The Associated Press