The new president of Cyprus, Demetris Christofias, is holding talks with Turkish Cypriot leader Mehmet Ali Talat aimed at reunifying the divided island.
The two leaders shook hands before starting the talks
It is the first time the two men are meeting since Mr Christofias was elected president last month.
Both leaders are from the political left and have been optimistic about the chance to work towards a settlement.
Talks have been stalled since 2004 when Greek Cypriots rejected a UN peace plan that was backed by Turkish Cypriots.
Mr Christofias and Mr Talat shook hands at the start of their meeting in a UN buffer zone near the abandoned Nicosia airport.
"We will have Cypriot coffee together," Mr Christofias said, AFP news agency reports.
The question now is whether that goodwill can be translated into the elements of a solution, the BBC's Tabitha Morgan reports from Cyprus.
Both leaders have promoted contact between the Greek and Turkish Cypriot communities, but it is not clear how negotiations will proceed.
Mr Talat favours returning to the 2004 UN-backed plan. But because the plan was rejected by 75% of Greek Cypriot voters, Mr Christofias prefers discussions to build on an agreement reached in July 2006.
This focused on individual confidence-building measures and practical areas where progress could be made.
Before the talks, Mr Christofis said he hoped for a deal to open a crossing point at Ledra street, a pedestrian thoroughfare in Nicosia that runs along the city's dividing line.
The street has come to symbolise the partition of the island.
Our correspondent says that whatever route is decided, negotiations are likely to be long and complex, for - as Mr Christofias himself has said - this diplomatic initiative cannot afford to fail.
The talks are being moderated by the UN's special representative to Cyprus, Michael Moller.
The Greek and Turkish Cypriots have been divided since 1974, when Turkey sent troops into the north, after a coup by Greek Cypriots who wanted union with Greece.
The island's partition has long stood as an obstacle to Turkey's bid to join the EU. The Greek Cypriot south, which joined the EU in 2004, hold veto rights over Turkey's accession.