"Kovacevic will not be extradited," Jeremic told independent B-92 television.
"Serbia is a sovereign and democratic country with an independent judiciary," Jeremic said, suggesting U.S. authorities should hand over the case file so Kovacevic could be prosecuted in Serbia.
Kovacevic, 20, had been recruited to play basketball for Binghamton University in northern New York state, but fled the U.S. in early June after being charged in the beating of Bryan Steinhauer during a May 4 bar fight.
Steinhauer, 22, remains hospitalized.
"This case has dealt a serious blow to the already strained relations between Washington and Belgrade," Jeremic said, adding that next week during this visit to the U.S. he will apologize to American officials who have sought Kovacevic's return to a U.S.
court to face assault charges.
Serbia's pro-Western government, which took office last month, has pledged to improve U.S.-Serbian bilateral relations that have been strained over U.S. recognition of Kosovo's independence.
Jeremic said Serbia is investigating two consulate staffers who were removed from New York after allegedly helping Kovacevic obtain emergency travel documents that helped him flee after being freed on bail.
Jeremic said that "initial" investigation shows they had breached discipline and that they will face unspecified consequences.