Turkish Cypriots are pressing for concrete progress
Cyprus President Glafcos Clerides and Turkish Cypriot leader Rauf Denktash held a 90-minute meeting on Wednesday.
The United Nations envoy for Cyprus, Alvaro de Soto, described it as "a very encouraging start".
The two long-standing adversaries met at Nicosia airport, disused since 1974. It lies in the UN-controlled buffer zone.
"Everything has gone very well," said Mr Denktash. He will hold further meetings with Mr Clerides on Mondays, Wednesdays and Fridays at 1700 (1500GMT) at the airport.
The island has been divided since 1974, when Turkey sent in troops following a coup by Greek Cypriots backed by the former military government in Athens.
The prospect of the island's European Union membership has galvanised movement towards a settlement. With or without a solution, the EU is expected by the end of this year to name Cyprus as a future member.
The two leaders agreed to return to the negotiating table last month after a groundbreaking meeting in early December - their first such contact for four years. Since then they have met on several occasions.
There is no set agenda at the talks, but both sides are agreed that if good progress is made the outline of a solution could be on the table by June.
The economy of the Turkish Cypriots continues to suffer under the burden of an international embargo.
Turkish Cypriots want the island established as a two-state confederation - a status which would mean official acknowledgement of Mr Denktash's northern state, which is currently only recognised by Turkey.
The Greek Cypriots however, who enjoy international recognition as the legal government of the whole island, have rejected this proposal - insisting on a single state.
Other thorny subjects include the property rights of those Greek Cypriots who fled their homes in the north in 1974.
Dervis Eroglu, prime minister of the self-declared Turkish Cypriot state, said he believed an agreement could ultimately emerge from the talks.
"But that agreement will have to satisfy the Turkish Cypriot people," he said.