Lutfi Haziri, Kosovo Albanian delegation chief, told reporters on Monday: "Today we are focused on the agenda and looking forward to the results.
"We want the status resolved as soon as possible. Independence is coming and we are playing a positive role."
Diplomats say independence is almost certain, closing a chapter on one of Europe's most pressing diplomatic conundrums.
The two eight-member delegations of mid-level politicians and advisers sat at a horseshoe-shaped table in the imposing 18th-century Palais Daun-Kinsky, under the chairmanship of Austria's Albert Rohan, deputy to United Nations envoy Martti Ahtisaari.
Ahtisaari, a former Finnish president, held separate breakfast meetings with each side before the start of negotiations, due to run into Tuesday.
The sitting delegations posed stony-faced for photographers.
Martti Ahtisaari held separate
meetings with each side
There were no handshakes.
The encounter, delayed a month by the death of president Ibrahim Rugova, is the first since Ahtisaari was appointed in November to negotiate a deal on the territory, sacred to Serbs but 90% populated by Albanians who demand independence.
The province of two million people has been run by the United Nations since 1999, when Nato bombing drove out Serb forces accused of atrocities against ethnic Albanian civilians in a two-year war with separatist rebels.
Trying to break the ice, the meeting will skirt the hot issue of status and focus on how to devolve power to the 100,000 remaining Serbs, ghettoised and targeted for revenge since 1999.
Western diplomats have said independence hinges on Albanians offering Kosovo's minorities a viable future.
Soren Jessen-Petersen, Kosovo's UN governor, said on Sunday: "The majority population here in Kosovo has a right to expect that their aspirations will be met when status is decided.
"But it is equally important that the majority is seen to be committed ... on minority issues."
Jessen-Petersen: The majority
must commit to minority issues
British analyst and author Tim Judah told Belgrade's Danas daily on Monday that "it is now completely clear the talks are not about the status of Kosovo, but about the status of the Kosovo Serbs".
Serbia wants the creation of an autonomous Serb entity with strong ties to Belgrade.
Albanians say that is a code for ethnic partition, a concept ruled out by the West.
Pristina is offering a more modest devolution.
The Contact Group of major powers setting policy on Kosovo wants a deal on "final status" within the year.
Independence not favoured
Belgrade says independence is unthinkable.
Rich in Orthodox religious heritage, Kosovo holds almost mythic status for Serbs, central to their identity for 1000 years.
But Albanians say independence is non-negotiable after a decade of Serb repression in the 1990s.
The Contact Group has urged Belgrade "to bear in mind that the settlement needs to be acceptable to the people of Kosovo".
Western diplomats say this means independence, conditional on major concessions to Serbs and guaranteed by an EU-led supervisory body and extended Nato peacekeeping mandate.
Analysts warn of a nationalist backlash in Serbia, which also faces divorce from Montenegro when the tiny Adriatic republic holds a promised referendum due in April on dissolving their lop-sided union, the last remnant of Yugoslavia.