Wisner said that the United States was in favour of reaching a solution by this year's end.
"It is the firm view of the U.S. that a delay offers no advantages to any party," envoy Wisner was quoted by Reuters as saying in Belgrade after meeting the Serbian officials.
According to a press release issued by President Tadic's Office, "Serbia wants the continuation of the negotiating process and it will remain committed to all political means so as to reach a consensual and feasible solution for Kosovo".
PM Kostunica said that after the approval of Serbia's new constitution, any solution for Kosovo's future status must be in line with principles of international law and the United Nations' Charter, which guarantees sovereignty and territorial integrity of all UN member states.
He reiterated that it "would be absolutely invalid to unilaterally recognise Kosovo's independence".
During his visit to Pristina last week, Wisner said the sovereignty of Serbia over Kosovo was changed with the adoption of the United Nations Security Council's Resolution 1244.
"It is not a matter of Serbian sovereignty, which changed when the U.N. agreed on 1244," Wisner was quoted by Reuters as saying on that occasion.
Resolution 1244 was adopted in June 1999 after 78 days of NATO air strikes against Serb forces that were accused of atrocities and ethnic cleansing in Kosovo. The resolution placed Kosovo under U.N. stewardship.