Serbia has recalled its ambassador from Washington in protest at US recognition of Kosovo's independence, saying the US has "violated international law".
Prime Minister Vojislav Kostunica also threatened to withdraw envoys from other countries which recognised the territory's secession from Serbia.
Mr Kostunica said the envoy's recall was Serbia's "first urgent measure".
France, the UK, Germany and Italy have all recognised the new state following its declaration of independence.
In New York, Serbian President Boris Tadic made an impassioned appeal to the UN Security Council to reject Kosovo's declaration.
But the Council remained deadlocked over how to respond to Kosovo's declaration of independence, although Russia and China supported President Tadic, and the UN body failed to agree on any action.
Serbia has a powerful ally in Russia, the BBC's Jane Little reports from the UN, but other permanent members of the council - including the US, Britain and France - insist independence is legal and the only viable way forward.
With a council so divided, it is unlikely any resolution could pass in favour of Serbia or Kosovo, our correspondent says.
The leading European states which endorsed independence did so after a meeting of EU foreign ministers in Brussels in which it was agreed that Kosovo should not set a precedent for other states.
Spain and several other member states have withheld recognition because of concerns about separatist movements within their own borders.
Serbian media report that Belgrade's ambassadors to all states which recognise Kosovo's independence are being ordered home.
The Associated Press news agency quotes the foreign ministry as saying Serbia's envoys to France and Turkey have been withdrawn for "consultation until further notice".
President Tadic told the UN Security Council there were "dozens of various Kosovos in the world and all of them lie in wait for Kosovo's act of secession to... be established as an acceptable norm".
"If you cast a blind eye to this illegal act, who guarantees to you that parts of your countries will not declare independence in the same illegal way?" he asked.
Serbia's interior ministry has filed criminal charges against Kosovo Albanian leaders instrumental in proclaiming independence, accusing them of proclaiming a "false state" on Serbian territory.
In Belgrade, about 10,000 students marched in protest at the independence declaration, and Serb enclaves inside Kosovo also saw anti-independence rallies.
Serbian security forces were driven out of Kosovo in 1999 after a Nato bombing campaign aimed at halting the violent repression of ethnic Albanian separatists.
The province has been under UN administration and Nato protection since then.
Pledges of support
On Monday, Washington formally recognised Kosovo as a "sovereign and independent state".
STANCE ON RECOGNITION
For: Germany, Italy, France, UK, Austria, US, Turkey, Albania, Afghanistan
Against: Russia, Spain, Romania, Slovakia, Cyprus
In Brussels, EU foreign ministers adopted a compromise proposal from Spain, one of several countries which argue that Kosovo's independence is a breach of international law and will boost separatists everywhere.
The bloc set aside differences by stressing Kosovo's declaration was not a precedent for separatists elsewhere and pledging that the whole Balkan region would eventually join the bloc.
Unanimous recognition of Kosovo was never at stake at the meeting because the EU has no legal right to recognise new states, BBC European affairs correspondent Oana Lungescu notes.
The question was whether, despite their differences on recognition, Europeans could unite on how to bring stability in their backyard, after almost two decades of seemingly endless Balkan crises.
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This is an ugly victory for demographic warfare
It took hours of tortuous negotiations but the EU managed to pass the unity test, our correspondent says.
Kosovo, the ministers agreed, was a unique case and did not call into question international legal principles, such as territorial integrity.
The bloc's statement said the EU was ready to play a leading role in the Balkans, with a 2,000-strong police and justice mission headed to Kosovo and new measures to promote economic and political development in the region, including a donors' conference by June.
The EU foreign affairs chief Javier Solana said there was a total commitment to bring all the Balkan countries into the EU.
But Kosovo will not be able to get very close until it is recognised by all 27 members, and that may take a long time, our correspondent adds.
Among other countries to recognise Kosovo was Turkey.
Correspondents say this has symbolic significance because for centuries the Ottoman Turks ruled the Balkans, including modern-day Serbia and Kosovo.