Kosovo's first independent elections have ended peacefully, with the prime minister claiming his party won convincingly and some minority Serbs ignoring a call to boycott and casting ballots alongside ethnic Albanians.

The elections Sunday for city council and mayors in 36 municipalities were seen as a key test of the fledgling state's viability following its contested February 2008 declaration of independence from Serbia.

Preliminary results were expected later Monday.

Hours after polls closed, Kosovo Prime Minister Hashim Thaci claimed his party won in 20 of the 36 municipalities.

"Today we gave freedom, independence and democracy its full meaning," Thaci told his supporters.

The junior partner in the governing coalition claimed it won in several of Kosovo's areas, including the capital Pristina, while opposition parties contested Thaci's outright victory and urged waiting until final results come out.

Across Kosovo party sympathizers celebrated by honking their car horns, waving party flags and setting off fire crackers.

No major instances of unrest or fraud allegations were reported, though the run-up had been marred by tensions between rival ethnic Albanian parties, as well as the possibility of a boycott from the Serb minority. Stones were thrown Wednesday at Thaci's convoy, and there was an apparent assassination attempt Thursday on an opposition mayoral candidate.

Thaci had urged the country's 100,000 Serbs to ignore calls by Belgrade and the Serb Orthodox Church to boycott the vote, calling it a key test for his new nation. So far, 63 countries have recognized Kosovo, including the United States and most European countries. Serbia has vowed to block further recognition and has Russia's support.

"I'm sure we will have success and appreciate very much participation of all citizen, in particular Serbs of Kosovo," Thaci told The Associated Press after he voted.

More than 5,000 officers were on patrol during the vote, which was also the first organized by Kosovo officials. Previous elections were run by the United Nations, which took control of Kosovo in 1999 after NATO waged an air war to stop Serb forces' crackdown on ethnic Albanian separatists.

"This is the best of democracy, and I will do my duty as a citizen," said Zoje Bujupi, an ethnic Albanian.

The results of the council and mayoral races, largely run on local issues, were unlikely to upset the country's fragile political scene, as the ethnic Albanian leadership is eager to show it can handle its own affairs.

Election officials said 45 percent of the 1.5 million registered voters cast ballots, a slight increase from the 2007 election turnout when 40 percent voted. Kosovo's first U.N.-run poll in 2000 saw an 80 percent turnout.

"We are very happy with the flow of these elections," election official Nesrin Kumnova told reporters.

"We have no information of any big incidents that would damage the election."

It was unclear how many of Sunday's voters were Serbs, but some Serbs could be seen voting in areas surrounded by majority Albanians.

One Serb leader running for a mayoral seat ignored the call to boycott and cast his ballot in the Serb enclave of Caglavica, just outside the capital Pristina.

"This vote here shows that ... the fear ... is loosening its grip," Momcilo Trajkovic said. He said the fact that Serbs were voting was a sign of better times for the minority population, which decreased by a third after the war ended in 1999 and many left to live in Serbia.

Serbia's Foreign Minister Vuk Jeremic said Belgrade did not recognize elections organized by "the so-called Republic of Kosovo," but would not "retaliate" against the Serbs who take part.

"Kosovo is an integral part of Serbia, and it will always be so," Jeremic said.

In the ethnically divided town of Mitrovica, where less then 1 percent of votes were cast, a Serbian government official based in Kosovo suggested the Serb participation this year could signal a rift within the Serb minority. Some of Kosovo's Serbs still recognize the Belgrade government as their own.

"Today's election is a serious challenge for the Serbian authorities here," Oliver Ivanovic told The Associated Press. "In time it will be a test of confidence in Serbia's rule. The possible serious participation of Serbs in these elections could duplicate power on the ground, and that would be very dangerous."

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