Serbian President Boris Tadic said the Eulex mission was welcome in Kosovo, but "under two conditions: that it is preceded by a UN Security Council decision and that it does not implement the Ahtisaari plan, which includes Kosovo's supervised independence".
Mr Tadic was referring to the plan drawn up by former UN envoy Martti Ahtisaari, which envisaged the decentralisation of Kosovo and considerable autonomy for Kosovo Serbs.
The plan - backed by Western countries - has not been formally approved, due to Russian objections.
The Eulex had been due to start its work over the weekend, but Russia has blocked the handover, saying the move has not been approved by the UN Security Council.
Ceremonies mark the constitution coming into force
Pieter Feith, the EU's special representative in Kosovo, said the UN thought it was the right time to hand over power to the Kosovo government.
"We think this is a significant new period that is starting," he said.
"The secretary general of the United Nations has recognised realities on the ground and has decided to reconfigure the United Nations presence here and this will give the government full authority in all its competencies."
He added that it would be part of his role to help the government implement the Ahtisaari plan for the future of Kosovo.
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