Serbia says Kosovo is defying the United Nations
Serbia has called on the International Court of Justice (ICJ) to declare that Kosovo's declaration of independence in 2008 broke international law.
Serbian representatives outlined their case as the court in The Hague opened hearings on Kosovo's secession.
Kosovo responded by saying its independence was irreversible.
Serbia still considers Kosovo to be part of its territory, and is hoping a favourable ruling at the ICJ will stop it gaining international recognition.
Some 63 countries have recognised the independence of Kosovo.
They include the US and 22 of the 27 members of the European Union.
But more than 100, including Russia and China, have not. The United Nations has also withheld recognition.
'Pillar of identity'
Serbia's representative, Dusan Batakovic, argued in court on Tuesday that Kosovo's independence move challenged his country's sovereignty and undermined international law.
He said it was the UN Security Council that set up a provisional administration in Kosovo following the 1999 conflict, and that Kosovo was therefore defying the UN.
He also argued that Kosovo was "the historical cradle of Serbia and constitutes one of the essential pillars of its identity".
Representatives of around 30 countries will present arguments to the court. Some are expected to argue that allowing Kosovo to secede would set a precedent that might be followed by separatists in other countries.
But Kosovo argued in court that any attempt to reverse its independence could spark conflict.
"Kosovo's independence is irreversible and that will remain the case, not only for Kosovo, but also for the sake of regional peace and security," the territory's foreign minister, Skender Hyseni, told the court.
He said Kosovo was happy to talk to Serbia, but only to discuss practical issues, not independence. "There can be no going back," he said.
More than 10,000 people were killed in conflict in the late 1990s, as an insurgency by ethnic Albanian separatists in Kosovo was suppressed by the Yugoslav government of Slobodan Milosevic.
Nato responded by bombing Serbia into submission, after which Kosovo was placed under UN administration.
It is the first time the UN's highest court has examined whether a secession complies with international law.
Hearings are due to last until 11 December, but the verdict is not expected for several months.
The decision will not be legally binding, but is expected to influence whether other countries recognise Kosovo.