PM Thaci told supporters his PDK had won in 20 of 36 municipalities
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.
'Proclamation of independence'
The government had been keen to ensure both the majority Albanians and the Serb minority took part in voting. Security was tight, especially in Serb areas.
Voting passed off peacefully, with turnout among minority Serbs thought to be higher than expected in some areas. Officials put the overall turnout at about 45%.
On Monday Mr Thaci told cheering supporters in Pristina that the PDK's victory was a testament to "good governance in the republic of Kosovo".
The BBC's Mark Lowen in Priostina says that the most important development in this election is that the Serbs voted in some areas of Kosovo for the first time, leading to fresh hopes for multi-ethnic democracy in the territory.
The chair of the European Parliament's observer delegation, Doris Pack, said she was happy with the number of those who had voted, especially among Serbs.
The conduct of the poll showed "that Kosovo is on its way to becoming a very functioning state", she said.
Most of the 120,000-strong minority Serb population still opposes Kosovo's independence.
Serbia had urged Kosovo Serbs not to take part in the poll, for fear of legitimising Kosovo's independence, but some local Serb politicians said people should ignore that call.
Momcilo Trajkovic, who was running for mayor in the Gracanica enclave near Pristina, said the vote represented "a crossroads for Kosovo Serbs".
Ten years on from Kosovo's war, reconciliation between the two communities is slow, says our correspondent. Thousands of Nato peacekeepers are still stationed there.