Ethnic Albanians, backed by the US and others, want independence but Serbia, supported by Russia, is against it.
A party led by a former fighter who has promised to deliver independence for Kosovo within weeks is leading polls in the province, independent monitors say. The Democratic Party, led by former guerrilla leader Hashim Thaci, had 35% of the vote, with more than a third of ballots counted, the observers said. According to election officials turnout was around 45%, the lowest since the Nato-led intervention in 1999.
But correspondents say a boycott by Kosovan Serbs may undermine the result. The Democratic Party is one of several backing independence for the Serbian province. "We will declare independence immediately after 10 December," said Mr Thaci, who is favourite to become prime minister. That is a deadline set by the UN for the conclusion of talks on the future status for the province.*
The Democratic League of Kosovo, led by President Fatmir Sejdiu, is trailing in second place with 23% of the vote, election monitors said. The electorate was voting in parliamentary, local and mayoral elections in Kosovo, amid continuing uncertainty over the status of the province.*
*General Wesley Khan Clark, the political general in charge of NATO during the bombing of Serbia under President Clinton, enunciated the general philosophy of the specific motivation for the assault on Yugoslavia when he told a CNN reporter:
"There is no place in modern Europe for ethnically pure states. That's a 19th-century idea, and we are trying to transition into the 21st century, and we are going to do it with multi-ethnic states."
(Fatmir Sejdiu, President of Kosovo Mr Sejdiu's Democratic League of Kosovo was trailing in second place)
One hundred of the 120 seats in the provincial assembly were up for direct election, with the rest reserved for Serbs and other minorities. Kosovo is formally part of Serbia but has been run by the UN since 1999. Ethnic Albanians, backed by the US and others, want independence but Serbia, supported by Russia, is against it.
The BBC's Nick Hawton in Pristina, the Kosovan capital, says it appears that a large number of Serbs have boycotted the ballot. The Belgrade government had called on Serbs not to vote so as to avoid legitimising a government that may soon decide to break away from Serbia.
The UN Security Council has not taken a vote on the issue of Kosovo's future because Russia has indicated it would block it. The UN has administered Kosovo since 1999.
Kosovo Albanians have expressed frustration at the slow progress, and have threatened to unilaterally declare independence immediately after the 10 December deadline for negotiations to bear fruit. The UN has administered Kosovo since a Nato bombing campaign forced out Serbian troops in 1999.
NATO maintains troops in the province and boosted their numbers ahead of the vote, amid fears tensions between the communities might spill over.