"This case is a top priority for the U.S. government," Munter said in a statement.
"I met formally today with senior most officials in the Ministry of Foreign Affairs to formally request that Kovacevic return to the United States to face justice," Munter said.
"Serbian officials have assured us they are prepared to cooperate and we are currently exploring all possible options."
The two countries' treaties effectively bar them from extraditing their own citizens. But legal experts said loopholes could be found that would allow the return of the basketball player since he fled the U.S. to avoid prosecution.
The 6-foot-9-inch (2.05-meter), 260-pound (118-kilogram) Miladin Kovacevic, who was recruited to play basketball for Binghamton University in upstate New York, was arrested after a May 4 fight at a downtown Binghamton bar that left student Bryan Steinhauer near death.
Steinhauer, 22, remains in critical condition and has not regained consciousness since the attack.
New York congressmen have asked U.S. Secretary of State Condoleezza Rice to pressure Serbia to immediately help locate the 20-year-old basketball player and return him to the United States, or face possible sanctions.
U.S. police said Kovacevic was at the bar with friends when Steinhauer danced with one of their girlfriends. Witnesses told police the men exchanged words before a fight ensued. Kovacevic is accused of repeatedly kicking Steinhauer in the head.
After several weeks in jail, Kovacevic was released June 6 when his family posted US$100,000 (euro63,000) bail. He left the U.S. on June 9.
As a condition of his release, Kovacevic surrendered his Serbian passport, but Serbian Deputy Consul Igor Milosevic allegedly furnished Kovacevic with travel documents. The Serbian Foreign Ministry said Milosevic is facing disciplinary action for issuing the new documents.
"The case of Miladin Kovacevic, who is reported to have brutally beaten a fellow student half his size even after he was unconscious, and then fled the United States while awaiting trial, is shocking," Munter said in the statement.
"We are appalled at the behavior of the Serbian Consulate, which inappropriately issued an emergency travel document to Kovacevic after he was ordered to relinquish his passport and remain in the U.S. by the presiding judge," Munter said. "I am personally outraged by this tragedy, and by the suffering caused to Bryan Steinhauer and his family."
Kovacevic's family, in an interview with The New York Post from the Serbian town of Kula, said they had helped their son flee the United States because the "media circus" in New York had unfairly targeted him.
His father, Petar Kovacevic, was quoted as saying the student was "a victim of small-town values ganging up against a foreigner.
He was targeted because he was a Serb and a very large man."
Kovacevic's parents said he also has a Croatian passport that he used to return home and that no special arrangements were made.
