Serena Williams apologized on Monday for the abusive and threatening tirade she launched at a line judge in a semi-final loss to eventual champion Kim Clijsters at the US Open.

But the 11-time Grand Slam champion's actions, which have already brought fines of $10,500, remain under investigation by the Grand Slam Committee and could result in greater fines or suspension from future Grand Slam events.

"I really wanted to apologize sincerely," Williams said. "I think the lady was doing the best she could. She was just trying to do her job. I would like to give her a big old hug and put it behind us."

Williams called Saturday's outburst and the controversy that has swirled around it a humbling experience.

"It definitely is," Williams said. "If it wasn't I don't think I could learn from the past."

One day after issuing a statement in which she admitted she "let my passion and emotion get the best of me" and "handled the situation poorly" but did not apologize for the incident, Williams released an apology.

"I want to sincerely apologize first to the lineswoman, Kim Clijsters, the US Tennis Association and mostly tennis fans everywhere for my inappropriate outburst," the statement said in part.

"I handled myself inappropriately and it's not the way to act -- win or lose, good call or bad call in any sport, in any manner. We all learn from experiences both good and bad. I will learn and grow from this."

Williams and sister Venus won the women's doubles crown Monday. Fans cheered the US duo but booed when award ceremony host Patrick McEnroe tried to ask Williams about her apology.

"What I think the crowd is saying, Patrick, is 'Let's move on,'" Venus said.

That could be easier said than done with a Slam suspension possible from the continuing probe and the possible loss of Slam prize money. Serena Williams won $350,000 from her singles run and shared 420,000 more from doubles.

Bill Babcock, executive director of the International Tennis Federation and a member of the Slam administrative committee, said it will take several weeks to completely investigate the match-ending meltdown.

"It's a legal process so there's time for notice, so there are weeks if not more," he said. "There can be suspensions from Grand Slams and fines of up to $250,000 or more."

Venus would not say if she would play an event from which Serena was banned, saying, "It's hard for me to answer that question because I don't think we're even at that point."

Serena Williams ignored a question about whether she might need anger management, said she had not had time to think about a possible suspension and said she still could not recall exactly what she screamed at the line judge.

"I was in the heat of the moment," she said. "I don't remember some of the points in the match today much less something I said a couple days ago."

US Open and Grand Slam committee officials have reviewed videotapes of the confrontation and the bizarre end of the Clijsters-Williams match.

The line judge, a woman whose name has not been revealed by tournament officials, called a foot fault on Williams to give Clijsters two match points.

Williams walked toward the woman who made the call, waving her racquet before her, and launching into a profanity-laced tirade of threats that led to an unsportsmanlike conduct violation.

Because Williams had already received a warning after smashing her racquet following the last point of the first set, the penalty point she was assessed handed Clijsters a finals berth.