International forces have been providing security in Kosovo
UN Secretary General Ban Ki-moon has set out plans to start ceding UN functions in Kosovo to the EU, despite stiff opposition from Russia.
The announcement comes only days before the disputed territory adopts a new constitution, following its declaration of independence in February.
Russia has demanded that the UN head in Kosovo, Joachim Ruecker, be disciplined or sacked over the "scandalous" moves.
Moscow said such moves "must decisively be prevented".
Kosovo President Fatmir Sejdiu confirmed on Thursday that he had received a letter from Mr Ban.
He did not disclose its contents, but Reuters news agency said it had obtained a copy.
"It is my intention to reconfigure the structure and profile of the international civil presence to one that... enables the European Union to assume an enhanced operational role in Kosovo," Mr Ban says in the letter, according to Reuters.
Kosovo has been under UN supervision since Nato forces ousted Yugoslav forces from the Serbian province in the late 1990s.
Russia has backed its Serbian ally and opposed steps towards independence for Kosovo, including the handover of responsibility for security from the UN to the EU.
Mr Ban said the "reconfiguration" of the Unmik mission would not "prejudice to the status of Kosovo".
However, Russia said any change to a UN mission must involve the UN Security Council - where Russia holds veto power.
Meanwhile, Nato announced that its member states would train a new multi-ethnic internal security force in Kosovo.
A Nato spokesman said the new Kosovo Security Force would be 2,500 members strong, multi-ethnic, civilian-controlled, and lightly armed.