Kosovo declared independence on Sunday after an emergency session of parliament, with Prime Minister Hashim Thaci saying the new state would be "proud, independent and free."
The U.S and a large number of European countries are expected to recognize Kosovo's sovereignty later on Monday.
Serbian Prime Minister Vojislav Kostunica said on Sunday that Kosovo's declaration of independence "violates international order." China has expressed its "deep concern" with the situation. Three EU states, Cyprus, Romania and Slovakia, earlier informed other EU governments that they would refuse to recognize Kosovo.
"I call on all sides to reaffirm and act upon their commitments to refrain from any actions or statements that could endanger peace, incite violence or jeopardize security in Kosovo and the region," Ban Ki Moon said after emergency UN Security Council consultations called by Russia on Sunday.
A hand grenade was thrown at a UN court building in the mainly Serb northern Kosovan town of Mitrovica on Sunday night. There were no injuries. Meanwhile, in Belgrade, gangs of youths protesting against the secession of Kosovo carried on running battles with riot police all night, with 35 people reported injured. Symbols of 'Americanism,' including two fast food restaurants, were also reported to have been attacked by protestors.
The Serbian government has called for a massive demonstration against what it calls the establishment of the "false state" of Kosovo.
Ban Ki-moon also said the United Nations would continue "to implement its mandate in the light of the evolving circumstances," with the Security Council resolution on Kosovo remaining in force.
"Pending guidance from the Security Council, United Nations Mission In Kosovo (UNMIK) will continue to consider Security Council resolution 1244 (1999) as the legal framework for its mandate and will continue to implement its mandate in the light of the evolving circumstances," he said.
The announcement came against the background of a joint statement by the U.S. and European UN Security Council members, Belgium, the U.K., France, Italy and Croatia, which said the EU and NATO were ready to ensure stability and security in the province, a UN protectorate since 1999.
"We are determined to take up our own responsibilities, as states and through the EU and NATO, to secure stability and security in the region," Belgium's ambassador at the UN, Johan Verbeke, said.
NATO will hold a Council session later on Monday to consider the situation. Meanwhile, NATO Secretary-General Jaap de Hoop Scheffer has urged all parties involved "to exercise the maximum restraint and moderation."
Vitaly Churkin, Russia's envoy to the United Nations, said an emergency session of the UN Security Council, to be held on Russia's initiative at 8:00 p.m. GMT on Monday, would involve Serbian President Boris Tadic.
"We are happy to have insisted on such a format that will enable the Serbian president to present Belgrade's position to both the Security Council and to the whole world," Churkin said.
Moscow is deeply opposed to the unilateral declaration of independence by Kosovo. It has said that it contradicts international law, and sets a dangerous precedent for other secessionist regions. Both houses of Russia's parliament plan to adopt a joint statement on Kosovo's unilateral declaration of independence on Tuesday.
