THOUSAND OAKS, Calif. — With a public apology and another appeal for privacy, Tiger Woods acknowledged yesterday 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."

Woods' career — as a golfer, a pitchman and perhaps the most recognized athlete in the world — has been largely without blemish since he turned pro at age 20.

Three of his sponsors — Nike, Gatorade and EA Sports — expressed support or commitment to Woods. Gillette said it had no plans to change its marketing programs. AT&T declined comment.

In the most critical comment from a 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, Fla., 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.

In its final report released yesterday, the Florida Highway Patrol said Woods caused $3,200 in property damage, was not wearing a seat belt and was traveling 30 mph in a 25 mph zone.

The six-page report — which did not include statements from Woods, his wife or any witnesses — said Woods' SUV rubbed up against bushes, crossed over a curb, onto a grass median and into a row of hedges before striking the fire hydrant and a tree. Damage to his Cadillac Escalade was estimated at $8,000.

Far more damaging to his image was the Us Weekly cover story.

Grubbs told the magazine she met Woods at a Las Vegas nightclub the week after the 2007 Masters — two months before Woods' wife gave birth to their first child.

In the voice mail released by the magazine, a man says to Grubbs:

"Hey, it's, uh, it's Tiger. I need you to do me a huge favor. Um, can you please, uh, take your name off your phone. My wife went through my phone. And, uh, may be calling you. If you can, please take your name off that and, um, and what do you call it just have it as a number on the voice mail, just have it as your telephone number. That's it, OK. You gotta do this for me. Huge. Quickly. All right. Bye."

The Associated Press could not confirm Woods was the caller.

Woods' limited response after the crash — the first statement Friday spoke of a "minor accident" — fueled speculation about a domestic dispute.

"The stories in particular that physical violence played any role in the car accident were utterly false and malicious," Woods said. "Elin has always done more to support our family and shown more grace than anyone could possibly expect."

Woods acknowledged his celebrity status — 82 victories, 14 majors and the first $1 billion athlete — while maintaining his right to keep his personal affairs just that.

"But no matter how intense curiosity about public figures can be, there is an important and deep principle at stake which is the right to some simple, human measure of privacy," Woods said. "I realize there are some who don't share my view on that. But for me, the virtue of privacy is one that must be protected in matters that are intimate and within one's own family. Personal sins should not require press releases and problems within a family shouldn't have to mean public confessions."

According to Us Weekly magazine, Grubbs said she was 21 when first approached by Woods in Las Vegas. The magazine said that meeting "progressed into a clandestine on-and-off affair" that included hundreds of texts.

"I hope he can forgive me for doing this and I know he probably can't," Grubbs is quoted as saying. "Whatever happens with Elin, I hope Tiger and I can reconnect and remain good friends."