"We are not opposed to the European Union taking on part of the responsibility for what is happening in Kosovo," Vladimir Chizhov, envoy to the European Communities, said adding a European mission should be approved by a UN Security Council resolution and Belgrade.
Chizhov said UN Security Council Resolution 1244 was currently the only legal basis for an international presence in Kosovo, which authorizes the deployment of the United Nations Mission in Kosovo (UNMIK) and the NATO-led Kosovo Force (KFOR).
The Security Council has been divided on the future of Kosovo, which broke away from Serbia in February, with Russia insisting the international presence in the region should be agreed on with Belgrade.
On Friday, UN Secretary General Ban Ki-moon pressed ahead with his plan to gradually hand over the main UN powers to the Albanian-dominated region's government and to a 2,200-strong EU police mission to be deployed there.
Moscow said on Saturday Ban's proposal was "outside his jurisdiction." Belgrade said the plan does nothing to preserve Serbia's territorial integrity, and that Serbia would never recognize Kosovo's independence.
Kosovo - which has been under UN administration since NATO bombings ended a conflict between Serb troops and Albanian separatists in 1999 - has been recognized by 43 of 192 UN member states, including by the United States and major European powers.