Aides in Vienna on Thursday presented maps at the fourth round of direct talks which started in February.
The talks focused on the borders of new municipalities for the 100,000 remaining Serbs in Kosovo.
They are outnumbered in the province by two million ethnic Albanians pushing for independence from Serbia.
The shattered mining town of Mitrovica, scene of the worst clashes since the 1998-99 war, topped the bill.
The Serbs' last urban centre in Kosovo and a gateway to Serbia proper, Mitrovica has become the battleground for two opposing visions of Kosovo's future, and is seen as key to any lasting settlement.
Serb negotiators said the town should be officially divided at the Ibar river that has separated Serbs and Albanians for seven years.
Dusan Batakovic, the Serb negotiator, said: "North Mitrovica should be a separate municipality, perhaps joined with Zvecan."
Haziri (C) says integration of the
town will happen
The Albanians, fearing that a separate northern Mitrovica would form the hub of a breakaway northern Kosovo, want at least some reunification.
Lutfi Haziri, Kosovo Albanian chief negotiator, said: "We believe the integration of the town will happen and local elections will bring a mayor, under which the municipality will be run in the future."
Kosovo, a province of Serbia, has been run by the United Nations since 1999, when Nato bombing drove out Serb forces, ending the crackdown by Belgrade in a two-year war with Albanian separatists.
As in previous rounds of talks, agreement is unlikely.
The UN mediators led by Martti Ahtisaari, the former Finnish president, say they are seeking common ground on technical issues before broaching the crunch question of the province's final status, possibly by July.
The meeting, which runs into Friday, became bogged down over Serb demands for 17 municipalities based on a census from before the mass Serb exodus that accompanied the end of the war.
Ahtisaari, head of UN mediators,
says common ground is sought
The Albanians are offering five of the 30 municipalities which make up Kosovo.
Diplomats say Ahtisaari's team will draft a compromise blueprint that will largely reflect Mitrovica's ethnic split and the reality that many Serbs do not plan to return to Kosovo.
The Albanians face pressure to give the Serbs greater local powers, as a condition of clinching their own state.
In Mitrovica, where French soldiers and UN police have patrolled the dividing line since 1999, the Kosovo Albanians propose the creation of two "sub-municipalities" under one joint body headed by an international administrator.