The visit yesterday, only his third since the United Nations took control of the majority Albanian territory in 1999, took place during campaigning for a general election in Serbia on January. 21.
A UN decision on the Kosovo Albanians' demand for independence from Serbia is expected in the spring, and Kostunica has made preventing Kosovo's secession the centrepiece of his election campaign.
''In the year ahead of us, the main question is the preservation of Kosovo, which amounts to the preservation of Serbia,'' Kostunica told hundreds of Serbs in the northern half of the tense, divided town.
''Everything I have done in politics with the support of the people has been insignificant compared to the fate of Kosovo.'' UN police and NATO soldiers guarded the main bridge over the Ibar River that divides Serbs and ethnic Albanians in the rundown former mining town.
Mitrovica has seen some of the worst clashes since 1999, when NATO bombing drove out Serb forces accused of civilian killings and ethnic cleansing in a two-year war with guerrillas.
Ten thousand Albanians were killed and NATO's deployment was accompanied by a wave of revenge attacks that forced tens of thousands of Serbs from their homes.
Kostunica saw in the New Year at the home of the Lazarevic family, which fled the western town of Klina in 1999. He returned to Belgrade early today.
UN envoy Martti Ahtisaari is due to present his proposal on Kosovo's fate after the Serbian election, having delayed it at the request of Western powers to avoid making Kosovo's possible independence an election winner for ultranationalists.
Diplomats say his blueprint will open the door to a form of independence supervised by the European Union and NATO. However, Russia, which has a veto in the U.N. Security Council, has threatened to block any settlement to which Serbia does not agree.
The EU, too, appears split, with some members looking nervously at the possible implications that independence could have for international law and other breakaway regions.
The UN mission and 17,000-strong NATO-led peace force is braced for possible violence should Kosovo's 2 million Albanians see their bid for independence delayed indefinitely.
REUTERS MS PM1713