NEW YORK – Jason Giambi will meet with George Mitchell, agreeing right before baseball commissioner Bud Selig’s deadline Thursday to cooperate with the steroids investigator.

Giambi, who for the first time publicly admitted he had a “personal history regarding steroids,” will become the first active player known to speak with the former Senate majority leader. No date was set for their session.

The New York Yankees star announced his decision after he spoke on the phone with Selig. Lawyers for the players’ union and Major League Baseball reached a written agreement that set rules for the meeting.

The former American League MVP said he wouldn’t implicate other players and appeared to backtrack on earlier remarks that the sport owed fans a collective apology for the steroids era.

“I alone am responsible for my actions and I apologize to the commissioner, the owners and the players for any suggestion that they were responsible for my behavior,” Giambi said in a statement.

Selig said the meeting with Mitchell will take place “promptly.” Following remarks by Giambi that seemed to be an admission of steroids use, the commissioner had threatened discipline if he didn’t talk to Mitchell.

Selig again left open the possibility of punishment.

“I will take Mr. Giambi’s level of cooperation into account in determining appropriate further action,” he said.

Giambi’s decision came two weeks after Selig requested the meeting and followed contentious negotiations between management and union lawyers. As late as Thursday morning, it remained unclear to some in the talks whether an agreement would be reached.

Selig called Giambi’s cooperation an “important step forward” in Mitchell’s efforts to provide a comprehensive report on the use of performance-enhancing drugs in baseball. But by pressuring Giambi to testify, Selig may have made other players even more reticent to discuss steroids.

Mitchell’s investigation, which began in March 2006, has gone more slowly than he expected, and the former senator declined to comment on the agreement. Giambi said there were boundaries on what he would tell Mitchell.

“I will address my own personal history regarding steroids. I will not discuss in any fashion any other individual,” Giambi said.

Giambi is in the sixth season of a $120 million, seven-year contract with the Yankees. He hasn’t played since May 30 because of a foot injury and it is not known when he will be able to play again.

Arn Tellem, Giambi’s agent, described Wednesday’s conversation between his client and Selig as “open and heartfelt.”

“The commissioner was extremely persuasive in impressing upon us how important he felt it was that Jason speak with the senator,” Tellem said.

Tellem said Giambi’s decision not to discuss other players “tracks the approach Jason has always taken throughout: to not point fingers, to not deflect blame, but rather to accept responsibility for his own behavior.”

Giambi testified to a federal grand jury in 2003 that he used steroids during the 2001-03 seasons and human growth hormone in 2003, the San Francisco Chronicle reported in 2004. He made a general apology before spring training in 2005 but didn’t specify what he was apologizing for.

His latest troubles began when he was quoted in USA Today last month discussing steroid use in baseball _ during a period when the sport did not penalize most first-time drug offenders.

“A direct conversation the commissioner impressed upon me the idea that the game of baseball would be best served by such a meeting,” Giambi said. “I will continue to do what I think is right and be candid about my past history regarding steroids.”

If Selig disciplines Giambi, there is a good chance it would be overturned by an arbitrator as lacking “just cause,” the standard set by baseball’s labor contract. Even though it appeared Giambi had the better legal position, he didn’t want a fight.

“I did not want to put my family through a lengthy legal challenge in support of my position,” he said. “In addition, the uncertainty of my playing status could detract from the efforts of our team to win the American League East. My focus at this time needs to be on rehabbing my injury, getting back on the field and contributing to the goals of my team.”

In the USA Today story on May 18, Giambi was quoted as saying: “I was wrong for doing that stuff. What we should have done a long time ago was stand up _ players, ownership, everybody _ and said: ‘We made a mistake.’ We should have apologized back then and made sure we had a rule in place and gone forward. … Steroids and all of that was a part of history. But it was a topic that everybody wanted to avoid. Nobody wanted to talk about it.”

Five days later, he was summoned to baseball headquarters in New York and was interviewed about those statements by three management lawyers.

“In the opinion of my representatives, (Giambi) was fully cooperative and candid in explaining his personal involvement with performance-enhancing substances,” Selig said.

While Yankees pitcher Mike Mussina said a Giambi-Mitchell meeting “will be interesting,” Rockies player representative Josh Fogg didn’t think Giambi will provide many breakthroughs.

“He’s been pretty upfront in what he’s said already,” Fogg said. “He’s already put it out there everything he’s done, so I don’t think he’s got anything to hide.”