Pristina: Prime Minister Hashim Thaci claimed victory late Sunday for his Democratic Party of Kosovo (PDK), but the main opposition Democratic League of Kosovo (LDK) claimed they led the vote.
"Victory is ours!" Thaci told his supporters hours after polling closed in what were the first elections since the territory declared independence nearly three years ago.
The election commission will only begin announcing results on Monday but an exit poll put the PDK in the lead with 31 percent of the vote.
Another count, by the Kosovo Democratic Institute (KDI), a leading election monitor, whose monitors counted the votes in 37 percent of polling stations, put the PDK ahead with 34.4 percent and the LDK trailing with 25.3 percent.
But the LDK insisted it was ahead in the vote.
"(The exit poll) is not a final result. The LDK is still leading at the Kosovo level," party spokesman Arben Gashi said.
This was based on a count by LDK election monitors of more than 60 percent of ballots cast on Sunday, he said.
Preliminary final results by the Central Electoral Commission are not expected until 24 hours after the polls close, which would by 7:00 pm (1800 GMT) Monday.
The streets of Pristina quickly filled up with rival PDK and LDK supporters honking their horns and waving flags.
Kosovo police were doing their best to keep the two sides apart but the tension was rising, with PDK supporters ripping up posters of LDK leader Isa Mustafa.
Mustafa called on his supporters not to protest in the streets but to remain calm while the votes were being counted.
"We only accept the results of the Central Electoral Commission," he said in a televised appeal.
"There is no need for our supporters to take to the streets because it will affect the counting of the votes. I appeal to our followers to keep the peace and order until the job is finished," Mustafa, who is also the mayor of Pristina said.
Sunday vote were Kosovo`s first elections since its 2008 unilateral declaration of independence.
Minority Serbs in the north of the Albanian-majority territory largely boycotted the poll, as urged to by Serbia, with tensions leading officials to close voting stations there three hours ahead of schedule.
Voting however passed off without incident although the electoral commission put the overall turnout at only 47.8 percent.
Serbia, which views the territory as its southern province and does not recognised its independence, had also urged Kosovo`s 120,000-strong Serb minority not to vote.
But while Serbs in North Kosovo maintained a virtual total boycott, Serbs in enclaves in central Kosovo, were reported to have turned out in unprecedented numbers, including up to 50 percent in some Serb towns.
They make up two-thirds of the Serb population.
The high turnout means that the Kosovo Serbs could be entitled to up to 15 seats in the 120-seat Parliament, giving them a kingmaker position as any party will have to put together a coalition to govern.
Analysts have warned that even if Thaci`s managed to remain the largest single party, he might not be able to govern as he would have difficulty finding coalition partners.
"It might be a Pyrrhic victory," political analyst Krenar Gashi said. "It will be very difficult get the (absolute) majority in the Parliament.”
"The very fact that the three main parties that can be considered for coalition are against coalition with Thaci shows that he lost the elections politically," he explained.
KDI estimates -- and an exit poll conducted by NGO Gani Bobi, together with political analyst Shkelzen Maliqi -- suggested that the Alliance for the future of Kosovo (AAK) and the Alliance for a New Kosovo (ARK) would keep their parliamentary presence.
The AAK is led by former prime minister Ramush Haradinaj, an ex-guerrilla leader currently detained by the UN war crimes court in The Hague awaiting a retrial. The ARK is run by construction tycoon Bexhet Pacolli.
Newcomers the Self-Determination party of populist activist Albin Kurti looked set to become the third biggest party of Kosovo.
European and international observers are expected to comment Monday on voting process.