He added that to be legal, secession required either an agreement between the parties or a UN Security Council resolution.
Other major EU states such as Britain and France do support Kosovo's declaration of independence, made on Sunday.
But even the attitude of some of the EU's major powers has been cast into doubt, after Germany, one of the main backers of Kosovo's break with Serbia, announced it was delaying a decision on whether to regonise the new state.
"We will not take a decision today on recognising Kosovo's independence," Angela Merkel, the German chancellor, said in Berlin.
She said Germany would wait for the EU foreign ministers meeting "to put in place a platform that will allow each member to take a position".
On Monday, Serbian police filed criminal charges against Kosovo's leaders for "organising the proclamation of a phoney state on Serbian territory".
Serbia's interior ministry said in a statement that Fatmir Sejdiu, Kosovo's president, Hashim Thaci, the prime minister, and Jakup Krasniqi, the parliamentary speaker, had been charged.
It accused the three of committing a "a serious criminal act against the constitutional order and security of Serbia".
In Kosovo, Serb groups led by the Serb-dominated north and with the full backing of Belgrade, Serbia's capital, rejected Kosovo's secession.
Tensions increased in Serb-controlled areas of Kosovo on Monday as thousands of Kosovo Serbs attended a protest in one of Kosovo's northern towns, demonstrating against Kosovo's independence.
Many chanted "This is Serbia" and some carried banners reading "Russia Help!"
A UN car was torched overnight in the northern Serb town of Zubin Potok, witnesses said.
In an earlier incident, hand grenades were lobbed at EU and UN buildings in the Serb stronghold of Mitrovica.
Serbia and Russia, neither members of the EU, have also objected to Kosovo's independence, with Russia warning that the secession would have repercussions in breakaway regions across the world.
|Thousands of ethnic Albanians celebrated as|
Kosovo declared its independence [AFP]
China, which has claimed self-ruled Taiwan as its own since the two split in 1949, has also said it is "deeply concerned" by the development.
Per Stig Moeller, the Danish foreign minister, attending the EU meeting on Monday, said he hoped the EU would find a "common platform ... so that we can have a common position towards Kosovo and also Serbia".
"It's very important that Serbia knows that it's not going to be a part of Russia, that it is going to be a part of Europe," he told reporters.
Olli Rehn, the European enlargement commissioner, who was also attending the talks, said it would be up to each state to decide whether to regonise Kosovo.
"The European Union will not take a decision as such but it will of course hold a responsible debate on the matter today," he said.
"Then it will be up to the individual EU member states to decide on the matter of recognition."
Most of the EU's 27 members are expected to recognise Kosovo and will provide a 2,000-strong force that will take over supervision of the new state from the UN.
But Barnaby Phillips, Al Jazeera's correspondent in Pristina, said the EU remained divided.
"What we expect will happen is the big western powers ... will be pushing for very fast recognition of an independent Kosovo," he said.
"But the EU is not entirely united ... some are very nervous about what is going on in Kosovo at the moment."
Prime minister Thaci announced on Sunday that "from today onwards, Kosovo is proud, independent and free", after all 109 deputies present a special session of parliament voted to declare independence from Serbia.
Thousands of ethnic Albanians took to the streets of Pristina, the main city, for the historic moment.
Revellers danced in the streets and waved red-and-black to celebrate the birth of the world's newest country. Some fired guns into the air.
But at the same time in Belgrade, up to about 2,000 demonstrators took to the street and stoned the US embassy in protest against its support of independence for Kosovo.
The US recognised Kosovo's independence on Monday, with George Bush, the US president, announcing that "the Kosovars are now independent".
He said independence for Kosovo was "something that I've advocated along with my government".