PRISTINA, Serbia, March 31 (Reuters) - Around 1,000 Kosovo Albanian hardliners rallied in the capital, Pristina, on Saturday to demand full and immediate independence from Serbia.

The protest passed peacefully, unlike in February when two ethnic Albanians died and dozens were injured in clashes between demonstrators and United Nations police.

The protesters reject a Western-backed plan drafted by U.N. envoy Martti Ahtisaari, which offers Kosovo independence but provides for an open-ended period of European Union supervision and broad self-government for the 100,000 remaining Serbs.

Speakers called on the U.N. mission running Kosovo since 1999 to leave, and branded Kosovo Albanian leaders "traitors".

"Why don't they let us hold a referendum? Because they know the outcome," protest leader Glauk Konjufca told the crowd outside the Kosovo parliament. Turnout was significantly down on previous protests by the same activists.

The southern Serbian province, 90-percent populated by ethnic Albanians, has been run by the United Nations since 1999, when NATO bombs drove out Serb forces accused of atrocities in a two-year war with Albanian separatist guerrillas.

Kosovo Albanian leaders have accepted the Ahtisaari plan, which is due to come before the U.N. Security Council next week.

It is backed by the United States and major EU members, but diplomats are concerned that continued Russian resistance could cause deadlock at the Council and trigger unrest in the impoverished province.

Washington wants a new U.N. resolution by June.

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