Kosovo's election commission is set to announce the result of the first poll since the country declared independence from Serbia last year.
PM Hashim Thaci assured supporters after polls closed on Sunday that his Democratic Party of Kosovo (PDK) had won 20 of 36 contested municipalities.
President Fatmir Sejdiu's Democratic League of Kosovo (LDK) said it had won the mayoral race in Pristina.
Official results are expected in the next few hours.
The vote was seen as a crucial test of the democratic credentials of Kosovo's young government, and observers are expected to give their verdict on whether polling met international standards - a crucial goal in Kosovo's search for wider recognition.
It has so far been recognised by 63 out of 192 UN members, and if the election is deemed to have been free and fair, that figure may increase, says the BBC's Mark Lowen in the capital Pristina.
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