Voting also took place in Serbia and Montenegro.
A total of 1.412 million eligible voters could choose among 22 political parties, six coalitions and six civic initiatives which ran for 100 seats in Kosovo's 120-seat Parliament. The remaining 20 seats are reserved for the Serb and other minorities in the province.
The turnout of ethnic Albanians and all other non-Serb minorities was satisfactory, organisers said. Local Serbs, however, boycotted the voting despite numerous calls to the contrary made recently by top international community officials, Serbian President Boris Tadic, and representatives of Kosovo institutions.
Kosovo Serbs said the U.N. and NATO had not created conditions for the Serb minority to live freely and without fear.
The elections, which were held in a peaceful atmosphere, were observed by close to 12,000 local and international observers, while security was provided by local police and the NATO-led Kosovo Force.
According to public opinion polls, President Ibrahim Rugova's Democratic Alliance may be expected to remain the strongest parliamentary party, followed by Hashim Thaqi's Democratic Party, and the Alliance for the Future of Kosovo.
The first preliminary results will be released on Monday, while the final results will be released between October 29 and November 7. The law stipulates that the results have to be verified by the U.N. civil administrator in Kosovo in order to be internationally recognised.