The UN General Assembly has unanimously adopted a resolution calling for dialogue between Serbia and Kosovo.
The resolution opens the way for direct talks between the two sides – the first since Kosovo declared its independence from Serbia in 2008.
It also drops earlier Serbian demands to reopen negotiations on the status of its former province.
The European Union and the United States have already recognised Kosovo’s independence.
The resolution replaced an original text in which Serbia rejected Kosovo’s secession.
That demand was removed after Serbia was warned that such a stance would endanger its ambition to join the EU.
The BBC’s Mark Lowen in Belgrade says the adoption of the UN resolution means Serbia has in effect given up its diplomatic fight for Kosovo.
Although Belgrade says it will never recognise Kosovo’s independence, the first direct talks between the two sides are now likely to follow.
Serbian Foreign Minister Vuk Jeremic finished his speech at the UN by saying his country was “looking to the future”.
There is now the feeling that this is the beginning of the end of the Kosovo problem, our correspondent says, as all sides are trying to resolve one of Europe’s most intractable conflicts.
Any talks between the two will be organised by the EU from Brussels.
Both Serbia and Kosovo want to become members of the European Union.
In July the International Court of Justice ruled that Kosovo’s declaration of independence did not break international law.
Serbian troops were driven out of Kosovo in 1999 after a Nato bombing campaign aimed at halting the violent repression of the province’s ethnic Albanians, who constituted 90% of its two million population.
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