International monitors say they are generally happy with the way Kosovo's local elections were conducted.
European monitors said the poll - the first since the country declared independence from Serbia last year - met many international standards.
PM Hashim Thaci says his Democratic Party of Kosovo (PDK) won 20 of 36 contested municipalities on Sunday.
President Fatmir Sejdiu's Democratic League of Kosovo (LDK) said it had won the mayoral race in Pristina.
The vote was seen as a crucial test of the democratic credentials of Kosovo's young government, and important for Kosovo's search for wider recognition.
It has so far been recognised by 63 of the UN's 192 members.
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