WASHINGTON, May 28 (Reuters) - President George W. Bush and Russian President Vladimir Putin spoke by phone on Monday and the White House said they agreed to keep talking about the U.N.-run Serbian province of Kosovo.

Bush and Putin are to see each other at a Group of Eight summit in Germany next week amid strains in U.S.-Russian relations.

"President Putin initiated the call. They discussed the importance of continuing their dialogue on Kosovo and other issues of mutual concern. The two leaders said they look forward to seeing each other at the G8 summit next week," said Gordon Johndroe, spokesman for the White House National Security Council.

A Croatian daily newspaper, Jutarnji List, reported on Monday that Russia, the United States and European Union have reached a compromise on the future of Kosovo.

The newspaper said Russia would not veto a Western-backed U.N. resolution granting Kosovo independence if certain conditions were met.

Kosovo's ethnic Albanian majority is impatient for independence after eight years of United Nations stewardship, and has the backing of the United States and its European allies.

Serbia rejects a breakaway and has enlisted the aid of Russia, which has hinted it could veto a U.N. independence resolution now being pushed by Western powers.

U.S.-Russian relations have been strained recently, most notably over Putin's opposition to U.S. plans for a missile shield in Europe that he considers aimed at countering Russia but which Bush says is to counter the potential threat of missile attack from renegade states.

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