Ban Ki-moon made the proposal earlier Friday at a UN meeting also attended by Kosovo President Fatmir Sejdiu. Kosovo is not a member of the UN.
He said the proposal does nothing to preserve Serbia's territorial integrity and his country "will never recognize" the independence of the breakaway republic.
"Therefore the Serbian Republic cannot support the report by the General Secretary," he said adding "the international community led by the UN must keep its central role in maintaining peace and stability in Kosovo" until Kosovo's status has been finally determined.
Tadic also said Kosovo officials had refused to discuss Kosovo's status with Serbia.
Russia's envoy to the UN, Vitaly Churkin, told the UN that Moscow considered "unacceptable any actions that transferred the functions or property of the UNMIK" to the so called European Union Rule of Law Mission in Kosovo, EULEX.
He also said the EU representative in Kosovo Pieter Feith was not eligible to become the chief international representative in Kosovo, since under UN Security Council Resolution 1244 the post should be occupied by a representative of the UN Secretary General.
The U.S. ambassador to the UN, Zalmay Khalilzad, said the U.S. backed Ban Ki-moon's proposal, which was also welcomed by Kosovo's president.
Russia and Serbia insisted that the UN secretary general make no further moves on the issue without Security Council approval.
Kosovo unilaterally declared its independence from Serbia in mid-February. It has so far been recognized by 43 of the 192 UN member states, including the U.S. and the majority of EU states. Russia and China have refused to acknowledge its sovereignty.
