In second place was the long-dominant Democratic League of Kosovo with around 22 per cent, ahead of four other ethnic Albanian parties.
The election campaign was dominated by party pledges to tackle 60 per cent unemployment, minimal foreign investment and rampant corruption.
The bid for statehood was never in question.
Ethnic Albanians, supported by the US, want speedy independence from Serbia, but Serbia, backed by Russia, is vehemently opposed to it.
However, in a sign that many voters see little difference in their ability to improve daily life beyond the declaration of statehood, less than half the electorate of some 1.5 million turned out to vote, the lowest showing since the 1998-99 war.
Joachim Ruecker, UN administrator and Mazllum Baraliu, election commission chief, said turnout was likely to be "between 40 and 45 percent".
The vote was also marred by an overwhelming boycott by the Serb minority, under orders from Belgrade not to legitimise a parliament threatening to declare independence within weeks.
Steve Schuck, a retired US army officer who is the deputy head of the UN mission in Kosovo (Unmik), told Al Jazeera that Serbs were being prevented from choosing the institutions that will represent them.
"I am disappointed by all the intimidation and humiliation which is keeping Serbs away from here," he said.
With independence expected to declared in the near future, Schuck said: "If there has ever been a critical time for Kosovan Serbs to vote, it is now."
There were no voters in nearby Leshak when the UN team arrived at about midday.
On the eve of the election, the home of a Serbian politician in the north was targeted in a Molotov cocktail attack, Veton Elshani, a police spokesman, said.
"The explosion damaged a car in the garage. We don't know what is behind the attack," he said.
Overall, turnout was modest among ethnic Albanians too, who have grown suspicious of political parties and unfulfilled promises of jobs and economic development.
Thaci, a former leader of the political wing of the KLA, had earlier pledged independence for Kosovo on Saturday.
"These elections are not about Kosovo's status," he said after casting his ballot.
"We will declare independence immediately after December 10."
That is the date for a report by Russian, United States and European Union mediators on efforts to find a compromise between Serbia and Kosovo's 90 percent ethnic Albanian majority.
Despite two negotiating sessions set for Brussels and Vienna in the coming week there is still no glimmer of a deal.
Kosovo has been run by Unmik since mid-1999 when a Nato offensive drove out forces loyal to Slobodan Milosevic, the late Yugoslav president, over a brutal crackdown on the KLA and its civilian supporters.
One hundred of the provincial assembly's 120 seats were up for direct election, with the remainder reserved for Serbs and other minorities.
Around 150 observers from the Council of Europe and as many as 25,000 local monitors monitored the election for voting irregularities throughout the country.