The vote is seen as a test of the international community's efforts to build a multiethnic democracy in Kosovo.
Today's vote is being overshadowed by renewed ethnic tensions and calls for ethnic Serbs to boycott the election. About 1.4 million voters are eligible to choose among some 33 political groups and 30 independent candidates.
Twenty seats in the provincial parliament are reserved for minorities, including 10 for the Serbs, who are outnumbered 9-to-1 in Kosovo. Without a strong show of voter support, however, Serbs risk being left largely powerless in the Kosovo policymaking.
Pascal Fieschi, the head of the Kosovo mission of the Organization for Security and Cooperation in Europe (OSCE), urged all voters of Kosovo today to cast their ballots.
"What you are voting for is the future of Kosovo, it is your future, it is in your hands and it is in this ballot box. Use it," Fieschi said.
Kosovo's chief UN administrator, Soren Jessen-Petersen, has also called for the Serbs to participate in the poll, saying the election marked a "turning point" and would set the stage for a UN review of democracy standards early next year and possible talks on the province's final status.
Jessen-Petersen wrote in today's edition of the "International Herald Tribune" daily that "Kosovo Serbs need legitimately elected leaders who can engage with the challenges ahead."
Kosovo has been a UN protectorate since Serbian armed forces withdrew in 1999 after NATO launched a bombing campaign to protect the province's ethnic Albanians.
Kosovar Serbs have expressed security fears after 19 people died when mobs from the ethnic Albanian majority rioted through Serbian villages in March, the worst violence here since the 1998-1999 war.
More than 1,000 extra NATO peacekeepers have been deployed to Kosovo for the election, bringing the total number of the NATO-led Kosovo force, or KFOR, to over 19,000. Police were also out in force, with all 6,000 local officers on duty.
Ethnic Albanian parties demand complete independence from Serbia but Serbs and the government in Belgrade insist that the territory is an inalienable part of the former Yugoslav republic.
The nationalist Democratic Party of Kosovo, led by Hashim Thaci, is considered the main rival to President Ibrahim Rugova and his moderate Democratic League of Kosovo.
"What you are voting for is the future of Kosovo, it is your future, it is in your hands and it is in this ballot box. Use it."
Rugova said today the poll is important for the independence of Kosovo and its European integration.
"This is a great and important day toward the formal recognition of independence of Kosovo. We speak for an independent Kosovo and [a Kosovo that is] integrated in [the European Union], NATO and in friendship with the United States," Rugova said.
Thaci said he would reject any international proposal on a final status that provides concessions to Serbs.
Kosovar Albanians expect the new assembly to provide a provisional Albanian-dominated government that will prepare for final status talks with the UN, tentatively slated for mid-2005.
Many ethnic Albanian voters today expressed support for an independent Kosovo. But for others, the more pressing concerns are unemployment and economic hardships in a province largely dependent on foreign grants.
Ethnic Albanian voter Qerim Gashi told RFE/RL: "I expect the election will bring some change, especially to reduce unemployment and corruption, to establish a more fair system and better security situation."
More than 1,600 polling stations opened across the province at 0700 Prague time and were to close at 2000 Prague time , with some 12,000 local and international observers on hand to look for irregularities.
The central election commission in Kosovo said that in the first three hours, some 5 percent of voters had cast their ballots. It also said that there was no municipality in Kosovo "where the number of voters is zero."
The latest surveys suggest no party will win enough votes to control the parliament and form a government by itself. The first unofficial results are expected this weekend.
(RFE/RL's South Slavic and Albanian Languages Service contributed to this report)