The UN Security Council is meeting to discuss a controversial plan to give UN-administered Kosovo independence.
Mr Ahtisaari failed to get a deal between Serbs and ethnic Albanians
The meeting launches what diplomats expect to be many weeks of formal and behind-the-scenes discussions.
The UN faces all-out opposition from Serbia, which insists Kosovo must remain part of its territory.
The council will meet Serbian caretaker Prime Minister Vojislav Kostunica and Kosovo's majority ethnic Albanian president Fatmir Sejdiu separately.
The US and the European Union have given their backing to a comprehensive set of proposals drawn up by the UN's special envoy, Martti Ahtisaari, after Serb and Kosovo Albanian negotiators failed to reach agreement on Kosovo's future.
Mr Ahtisaari's blueprint gives Kosovo the independence its overwhelmingly ethnic Albanian population has been demanding since the break-up of the old Yugoslavia at the beginning of the 1990s.
At the same time, the proposals envisage extensive self-government for Kosovo's Serb-inhabited municipalities and continuing links between them and Belgrade.
BBC South-East Europe analyst Gabriel Partos says in many respects Serbs living in northern Kosovo would be barely aware that they were not in Serbia itself.
Leaders of Kosovo's nearly two-million-strong Albanian community have gone along with these provisions, just as they have accepted that initially their newly-independent state would be under the ultimate authority of an International Civilian Representative.
Serbia, for its part, has rejected the Ahtisaari proposals, with Mr Kostunica saying they violate the UN's Charter and amount to the amputation of 15% of his country's territory.
The US and the main EU countries believe there is no viable alternative to the Ahtisaari plan.
Our correspondent says there is concern that eight years after the UN took over control of Kosovo - following a decade of repressive rule from Belgrade that had culminated in brutal war - Kosovo's ethnic Albanians are getting restless and the increasing tension could lead to a flare-up in violence.
Serbia's ally Russia has repeatedly stated it will give its backing to a Kosovo settlement only if it is acceptable to both sides.
Russian ambassador to the UN, Vitaly Churkin, said on Tuesday it was "too early to speak about a resolution".
But French counterpart Jean-Marc de la Sabliere said the Ahtisaari plan should be adopted.
"We should not delay... It would be very risky. To keep the status quo is not an option."