United Press International, quoting a resident of Kiev, reported yesterday that the death toll at the site of the nuclear disaster in the Soviet Union north of Kiev may have surpassed 2,000.

The source of the report was as Kiev woman who has long provided accurate information, according to Sylvana Foa, the foreign editor of U.P.I. ''This source has never proved to be unreliable,'' she said.

The unidentified Kiev resident reported by telephone yesterday morning that between 10,000 and 15,000 people had been evacuated from Pripyat, the site of the Chernobyl nuclear reactor where the nuclear accident occurred.

''Eighty people died immediately and some 2,000 people died on the way to hospitals,'' said the Kiev resident. ''The whole October Hospital in Kiev is packed with people who suffer from radiation sickness.''