(Updates with U.S. ambassador Khalilzad, diplomats)

By Fatos Bytyci

PRISTINA, Serbia, June 4 (Reuters) - Kosovo said on Monday it expected the United Nations to grant it independence from Serbia "very soon" and urged Russia to drop its opposition to a Western-drafted Security Council resolution.

The United States repeated that it hoped for a U.N. Security Council vote this week, despite the risk of a Russian veto.

Western members last week circulated a draft text supporting a plan by U.N. envoy Martti Ahtisaari and effectively clearing the decks for a declaration of independence backed by Kosovo's 90-percent ethnic Albanian majority.

The United States says it hopes the Council will act "promptly" on the resolution, and that differences with veto-holder Russia should not be insurmountable.

Washington opposes Serbia's demand for a resumption of negotiations, saying it sees no indication that Serbia would negotiate in good faith or change its categorical rejection of independence, since the new Serbian constitution forbids it from even considering anything other than maintenance of sovereignty.

Asked by reporters when he expected the vote to happen, Kosovo Prime Minister Agim Ceku replied: "Very soon."

President Fatmir Sejdiu said: "We have seen the efforts of the international community, the European Union and the United States to come up with a new resolution supporting Ahtisaari's plan. We would like Russia to be part of this."

G8 SUMMIT

At the United Nations, diplomats from several countries said they expected the Security Council to await the results of the June 6-8 Group of Eight summit in Germany.

But U.S. Ambassador Zalmay Khalilzad said he was still anticipating a vote on the Kosovo resolution this week, as he had forecast last Thursday.

"We are still waiting to hear a substantive response from the Russians on the Kosovo resolution that was introduced last week, and our expectation is still to go to a vote this week," Khalilzad told reporters.

The sponsors of the resolution -- the United States, Britain and France -- would consult on the issue on Tuesday, he said.

The province of 2 million people has been run by the United Nations since 1999, when NATO bombs drove out Serb forces to halt the slaughter and expulsion of civilians in a two-year war with separatist Albanian guerrillas. Ten thousand people died.

NATO leads a 16,500-strong peace force in the territory, and Western powers fear delay could spark unrest by Albanians impatient for an end to their political and economic limbo.

Kosovo leaders had promised independence by mid-year. They have indicated they are ready to secede unilaterally if made to wait much longer. Diplomats say the US would support such a move, but the 27-member EU would almost certainly be split. (Additional reporting by Douglas Hamilton in Belgrade and Patrick Worsnip in New York)

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