The fight broke out during the last game of the Acropolis tournament, which was abandoned with 2:40 remaining and Greece leading by one point. The incident occurred just a week before the basketball world championship in Turkey, where both teams will play.
"This shouldn't have happened," said Serbian coach Dusan Ivkovic, who is due to take over Greek club Olympiakos next season. "Relations with the Greeks are now very bad."
A stunned crowd of about 5,000 at the Athens Olympic Arena watched players from both teams exchange punches and kicks on the floor and in the tunnels leading to the dressing rooms. Two or three spectators entered the fray but were quickly shoved out of the arena.
The fight began when Greece forward Antonis Fotsis moved threateningly against Serbia guard Milos Teodosic, who had fouled him. Krstic grabbed Fotsis by the throat and threw a chair toward Sofoklis Schortsanitis, who was pursuing him. The chair hit Yannis Bouroussis, who had not played because of a hand injury, and left him with a bloody wound on the side of his head.
The teams were finally separated after they had carried the fray off the court.
Prosecutor Costas Simitzoglou released Krstic pending an investigation into the brawl. Investigators from Greece's sports violence squad will examine video footage of the game and take statements from witnesses before deciding whether to bring charges.
Krstic returned to his hotel after being released and was due to leave Athens for Belgrade later on Friday. The rest of the Serbia team returned earlier.
"I don't know the rules, but I hope I won't be punished," Krstic told Serbian media. "An (act of) stupidity was committed, and I hope they will not punish us. The Greeks started the brawl, there were no guards and the (Greek) fans entered the court."
FIBA secretary general Patrick Baumann said in a statement Friday that the international basketball federation will conduct its own review of the violence.
"FIBA will take whatever steps are necessary against any individual player found to have been involved in this shocking incident," Baumann said. "FIBA wishes to make it clear that it will not hesitate from taking the strongest possible action against any individual found to have brought the sport of basketball into disrepute."
U.S. coach Mike Krzyzewski said he showed his team footage of the brawl as an example.
"We just told our guys that if something happens to walk away and not to pull anyone from another team, to just pull your teammate," Krzyzewski said in Madrid, where the Americans have been preparing. "This is not about getting into a fight but playing basketball — and you can be suspended. You represent your country so you shouldn't do that."
Krzyzewski said that Kevin Durant and Russell Westbrook, teammates of Krstic on the Thunder, were "surprised because he is such a quiet guy, smiling all the time."
Thunder general manager Sam Presti said he spoke with Krstic on Friday.
"He recognizes that this is an unfortunate situation and he is regretful for his actions," Presti said in a statement. "He has apologized to the Greek national team and has reached out personally to specific members of the Greek team. He is looking forward to continuing his preparation for the world championships and representing his country."
U.S. forward Lamar Odom said his team would avoid being carried away by their emotions when they face Greece in an exhibition game next week in Athens, and later during the tournament.
"We understand that if something like that were to happen with us it would be worldwide news," Odom said, "so that's something we won't let happen."
Greece's deputy culture and tourism minister Giorgos Nikitiadis, whose portfolio includes sports, condemned the "regrettable incidents."
Nikitiadis said Greek authorities would not tolerate sports violence, "especially from those who, although they wear their national symbols, are not aware that they represent their country — not themselves."
Serbia and Greece are scheduled to play in the basketball world championships beginning Aug. 28 in Turkey, although they are in separate groups for the preliminary round.
Serbia plays in Group A with Angola, Argentina, Australia, Germany and Jordan, while Greece, the runner-up at the last worlds in 2006, is in Group C with China, the Ivory Coast, Puerto Rico, Russia and Turkey.
Group B features Slovenia, Brazil, Croatia, Iran, Tunisia and the United States, and Group D contains Canada, France, Lebanon, Lithuania, New Zealand and defending champion Spain.
AP Sports Writer Paul Logothetis in Madrid and Associated Press Writer Dusan Stojanovic in Belgrade contributed to this report.