The election monitoring group "Democracy in Action" says that with votes from 90 percent of polling stations counted, Thaci's PDK is leading with 34 percent, beating the Democratic League of Kosovo (LDK) into second place with 22 percent.
The election result puts Thaci in a position to form a coalition government.
He has vowed that if he becomes prime minister, he intends to declare Kosovo independent from Serbia after December 10 -- the deadline for international mediators to report back to the United Nations on the progress of negotiations to resolve the dispute over Kosovo's future status.
The vote was boycotted by Kosovo's Serbian minority, which strongly rejects the ethnic Albanian plan for independence.
The United States has praised the peaceful conduct of the elections, but criticized the Serbian boycott of the vote.
(compiled from agency reports)
