Peter Egner, 88, who was born in Yugoslavia, is suspected of war crimes against Jews in Belgrade during the German occupation of Serbia, the Higher Court said.
Serbia had said it would seek Egner's extradition from the United States, where he has been living in a retirement community outside Seattle. Belgrade has worked closely with the U.S. authorities on the case.
Egner has been fighting U.S. federal government efforts to strip him of his American citizenship, which would pave the way for his extradition. U.S. officials say he did not disclose details from his past when sought citizenship in the 1960s.
Egner has denied the accusations, claiming he knows nothing about the Einsatzgruppe, a Nazi-run Serbian police unit that rounded up Jews, political prisoners and other enemies of the Third Reich in the wake of Hitler's attack on the Soviet Union in the early 1940s.
Allegations about Egner's Nazi past first surfaced in the U.S. two years ago.
The U.S. Justice Department, citing Nazi documents, said that in the autumn of 1941, Egner's unit executed 11,164 people - mostly Serbian Jewish men, suspected communists and Gypsies - and that in early 1942, it killed 6,280 Serbian Jewish women and children who were held as prisoners.
In two months, those women and children allegedly were taken from the camp and forced into a specially designed van, in which they were gassed with carbon monoxide.