Speaking in an interview with Dnevni Avaz, a popular daily published in Sarajevo, Sutanovac said: "I have said many times that the Kosovo problem cannot be resolved militarily."
"When we tried to resolve problems in the former Yugoslavia by deploying the army, we encountered even greater problems," the minister said.
The Albanian-dominated Serbian province has been a UN protectorate since the NATO bombing of the former Yugoslavia ended a conflict between Albanian and Serb forces in 1999.
The UN Security Council failed last year to bridge divisions over Kosovo's future. Belgrade is opposed to the region's independence, and has offered it broad autonomy within Serbia. Pristina insists on full sovereignty, however.
Most Western states have backed the volatile area's drive for independence, and said recently that Kosovo's status would now be determined by the European Union and NATO. Russia insists that Belgrade and Pristina continue to try to reach a compromise.
The UN Security Council is to discuss a report on Kosovo by UN Secretary General Pan Ki-Moon on January 16.
Sutanovac said the Serb army could help international peacekeepers in Kosovo should they ask for help. "The appearance of Serb troops in Kosovo without invitation would be tantamount to declaring war on KFOR forces and the entire international community," he commented.
He also said Belgrade should not become alienated from NATO, and should seek ties under a Partnership for Peace program, although it should not aspire to full membership in the alliance.