But while the four major EU powers – Britain, France, Germany, and Italy – announced they would recognise the new state, Spain and several other countries which have problems with their own separatist groups said they would not do so.
Russia warned it would set a dangerous precedent for separatist groups worldwide.
Ninety per cent of Kosovo’s two million people are ethnic Albanian – mostly secular Muslims – who saw no reason to be part of Christian Orthodox Serbia.
As word of the recognition spread, cheering ethnic Albanians poured into the streets of Pristina.
But tensions flared in northern Kosovo, home to most of the territory’s minority Serbs.
An explosion damaged a UN vehicle outside the ethnically divided town of Kosovska Mitrovica, where thousands of Serbs demonstrated, chanting "This is Serbia!"
Serbia is preparing to ask the UN Security Council to condemn Kosovo’s declaration of independence as illegal, and last night it recalled its ambassador to the U.S. in protest against Washington’s recognition of the breakaway state.
Spain, like Russia, is grappling with its own separatist movements and believes it would not be in its interest to back the former territory of Yugoslavia.
"The government of Spain will not recognise the unilateral act proclaimed yesterday by the assembly of Kosovo," Spanish Foreign Minister Miguel Angel Moratinos told reporters on arrival for a meeting of EU foreign ministers.
He said that to be legal, secession from Serbia required either an agreement between the parties or a UN Security Council resolution.
Britain’s Foreign Secretary David Miliband said it was "critical" for the European Union to show leadership on the western Balkans and to maintain peace and stability there.
"I think it’s very important that we recognise that all of the countries in the Western Balkans are European countries," he said.
"It is critical that Europe shows real leadership in how it ensures that peace and stability are the order of the day in the Western Balkans."
Aside from Spain, at least five – Cyprus, Greece, Slovakia, Bulgaria and Romania – have indicated they will not recognise Kosovo due to legal misgivings or concern about restive minorities in their own countries.
EU foreign policy chief Javier Solana urged restraint after Serbian nationalists stoned Western embassies in Belgrade in anger at the declaration of independence by Kosovo’s Albanians.
"The EU has already decided to send a mission, a mission of stability, a mission of rule of law.
It should contribute to the stability of the Balkans," Solana told reporters.
The EU agreed on Saturday to send 2,000 police, justice and civil administrators to help build Kosovo’s institutions.
NATO said in a statement its 17,000-strong KFOR stabilisation force would "respond resolutely to any attempts to disrupt the safety and security of the population of Kosovo".
EU Enlargement Commissioner Olli Rehn said Kosovo was a unique case and would not set a precedent.
He praised Kosovan leaders for promising to respect minority rights in line with a plan drafted by former Finnish President Martti Ahtisaari.
Russia, Serbia’s closest ally, prevented the UN Security Council from adopting his blueprint for supervised independence last year.
That led Kosovo to declare statehood in coordination with Western powers.
Q and A
Why did Kosovo want independence?
Some 90 per cent of the population is Albanian. Demands for independence were ignored amid the wider Balkan wars of the 1990s until an armed rebellion was launched towards the end of the decade.
Serb forces hit back so hard in 1998 that 100,000 Albanians fled to the hills and Nato powers warned Serb leader Slobodan Milosevic they would not tolerate another round of "ethnic cleansing" in the Balkans.
Peace talks in France failed and in March 1999 Nato started bombing Serbia to force it to withdraw its forces from Kosovo. Some 800,000 Albanians fled or were expelled to Macedonia and Albania before Milosevic gave in 78 days later. As his forces pulled out, up to 200,000 Serbs and other ethnic minorities left as well.
How has Kosovo been run up to now?
Kosovo has been administered by the United Nations, with Nato troops as peacekeepers, since 1999. Unemployment is more than 50 per cent. Kosovo’s uncertain future has deterred outside investment.
Spasms of ethnic violence, mostly by Albanians against Serbs, and organised traffic of contraband and people, have tarnished its image.
What will happen next?
Following Sunday’s declaration of independence by the Kosovo parliament, the procedure is likely to follow a plan drawn up by UN special envoy Martti Ahtisaari for "supervised independence" which was rejected by Serbia.
Under the plan, a 120-day transitional period will follow a declaration and full independence would then come into effect.
How will the world react?
EU foreign ministers met in Brussels yesterday and the majority of member states were in favour of independence. Cyprus, Romania, Slovakia, Spain and Greece are not, fearing it could set a precedent for separatist groups in their own countries among other reasons.
Russia has firmly rejected the Kosovo move and wants the United Nations to annul the declaration.
Why is Russia so opposed?
Russia considers Serbia to share a Slavic and Orthodox Christian tradition and parts of the Belgrade government have actively courted Moscow’s support in recent months. Serbia’s oil monopoly was recently sold to Russia’s Gazprom for what was considered a low price.
Traditionally an ally of Serbia, Russia is concerned by the EU’s expansion into the Balkans and Moscow believes Kosovo would set a precedent.
There is little difference, according to the Kremlin, between the separatism of Kosovo and the ambitions of pro-Russian areas such as Abkhazia and South Ossetia in Georgia and Trans-Dniester in Moldova.
What will happen to Kosovo’s Serb minority?
An estimated 120,000 ethnic Serbs live in Kosovo, many in Serb-dominated areas north of the Ibar river, adjoining Serbia proper. Half of the population lives under Nato protection in scattered enclaves south of the Ibar river.
Under the Ahtisaari plan, the Serb minority would have guaranteed places in local government and parliament, proportionate representation in the police and civil service, and a special status for the Serbian Orthodox Church.
Is there a risk of violence?
Yes. Nato forces have stepped up their state of alert, especially in ethnically mixed areas of Kosovo. Commanders have promised more patrols.
The key question is whether they will be able to control flashpoints such as the main northern town of Mitrovica, where ethnic Serbs live north of the Ibar river and ethnic Albanians to the south.
Could the violence spread?
The nightmare scenario would involve Kosovo Serbs who live south of the Ibar river being violently driven from their homes, and the expulsion of ethnic Albanians living in enclaves in northern Kosovo, and in the Presevo and Bujanovac regions of southern Serbia.
It could go further than that. There are large ethnic Albanian communities in Macedonia and Montenegro, some of whom might seek a union with Kosovo.