"I expect us to make the biggest progress toward Europe in the next 13 months, (bigger) than any country in transition has ever made," Bozidar Djelic said.
Serbia, which faced years of international isolation during the Balkan wars, has remained among the last countries in the region to move toward membership the union.
European Union officials initialed a pre-membership deal with Belgrade earlier this month. But EU officials have said that formally signing that agreement hinges on the arrest of Gen. Ratko Mladic and other war crimes fugitives sought by a U.N. court.
Djelic said he expected Serbia to sign a Stabilization and Association Agreement in January, taking a crucial step toward formal candidacy.
The deputy premier added that authorities were doing all they could to capture Mladic and other suspects sought by the U.N. war crimes tribunal in The Hague, Netherlands.
Mladic is wanted on genocide charges for allegedly orchestrating the 1995 massacre of 8,000 Muslims in Srebrenica, Bosnia. Tribunal officials insist he is hiding in Serbia.