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"I just felt like as a man, it was important for me to tell him, 'I'm sorry it came out that way,' " Bryant said at a lightly attended news conference at Loyola Marymount, where he spoke mainly about his camp for youngsters at the school this week.
Bryant said that while he could have called Kupchak, it was important he speak with him face-to-face.
"I was frustrated, I was venting," Bryant said.
When asked whether he still wanted out, Bryant replied: "I haven't thought about that in a long, long time. I've kind of stepped away from that. I've concentrated on Team USA. What I say is what I say. We'll just have to see where it goes."
The U.S. national team begins practice July 20 in Las Vegas.
Bryant, the NBA's leading scorer the past two seasons, complained about a lack of talent around him at season's end, and said May 30 he wanted to be traded, adding nothing could change his mind.
Despite that request, the Lakers have made clear that trading Bryant isn't in their plans. Bryant is owed $88.6 million over the next four seasons, but could terminate his contract in two years.
The Lakers haven't won a playoff series since reaching the NBA Finals in 2004 for the fourth time in five years. With Bryant and Shaquille O'Neal leading the way, they won three straight championships from 2000-02.
O'Neal was traded to Miami in July 2004, a day before Bryant signed a seven-year, $136.4 million contract to remain with the Lakers, who haven't won a playoff series since O'Neal left.
Bryant said he hasn't spoken with Derek Fisher since Monday, when Fisher was released by the Utah Jazz so he can concentrate on finding the best care for his 11-month-old daughter, who has cancer in her left eye.
Fisher said he wants to live in one of the six or seven cities being considered for Tatum's care. Bryant and Fisher were teammates and, from all indications, good friends while playing with the Lakers from 1996-2004 -- the first eight seasons of their NBA careers.
Kupchak didn't rule out the possibility of a return to the Lakers for Fisher, who signed with Golden State as a free agent after the 2003-04 season and was later traded to Utah.
Bryant said 450 kids aged 8-to-18 attended his camp.