NICOSIA, Cyprus (AP) — The leaders of the ethnically divided east Mediterranean island of Cyprus are ready to meet with the U.N. secretary-general next month to map out possible next steps toward a resumption of formal reunification talks, officials said Friday.

U.N. spokesman Aleem Siddique said in a statement that the two would carry on discussions with U.N. envoy Jane Holl Lute to prepare the ground for “structured and results-oriented” negotiations leading to a peace deal “with a sense of urgency.”

Siddique issued the statement after Greek Cypriot President Nicos Anastasiades and Turkish Cypriot leader Mustafa Akinci held private talks for nearly four hours.

Anastasiades said after the talks inside a U.N. protected area that separates the internationally recognized Greek Cypriot south and the breakaway, Turkish Cypriot north that Lute’s contacts aimed at preparing a meeting with U.N. chief Antonio Guterres.

The hoped-for meeting with Guterres would take place after next month’s U.N. General Assembly session in New York and would size up prospects for a resumption of peace talks, two years after they collapsed at a Swiss Alpine resort.

An informal conference involving officials from Cyprus’ ‘guarantors’ Greece, Turkey and Britain would precede formal peace talks to ensure that all sides would be working toward the same goal.

“We have a good climate, we have a common basis on which talks can take place, but I must admit that disagreements remain on serious matters,” Anastasiades told reporters.

Numerous attempts at reaching a reunification deal over the past 45 years have gone nowhere.

Cyprus was split in 1974 when Turkey invaded following a coup by supporters of union with Greece and numerous attempts at clinching a peace deal since have gone nowhere. Only Turkey recognizes a Turkish Cypriot declaration of independence and keeps more than 35,000 troops in the north.

Greek Cypriots are wary of any deal that would put an envisioned federated Cyprus under what they see as the direct or indirect control of Turkey. They reject Turkish Cypriot demands for a permanent Turkish troop presence and veto power on all government decisions on the federal level.

Turkish Cypriots object to what they see as being relegated to junior powers in a new partnership and seek federal decision-making parity with the majority Greek Cypriots.

However, Akinci said he would take a closer look at Anastasiades’ proposal to cede more power to each federated part in the running of its own affairs.

Anastasiades repeated that peace talks can’t resume if Turkey doesn’t stop unlawful gas drilling in waters where Cyprus has exclusive economic rights.

Turkish vessels are currently drilling for gas on either end of Cyprus in response to the Cyprus government’s own gas search within its exclusive economic zone. Turkey doesn’t recognize Cyprus as a state and says that it’s only defending its rights and those of Turkish Cypriots to the area’s energy reserves.

Anastasiades repeated that a Turkish Cypriot proposal for a joint committee to manage gas drilling is a non-starter because it’s a matter for sovereign governments to decide what goes on in their territorial waters.

He said Turkish Cypriots’ rights to the island’s energy reserves are assured, but that he would be willing to brief Akinci on drilling developments.

Akinci said that’s not enough for Turkish Cypriots who insist on joint management, warning that Turkey and the Turkish Cypriots would carry on drilling if the Greek Cypriots continue their own gas search.

The Turkish Cypriot leader said he submitted a list of five additional confidence-building measures that could be implemented, including the establishment of a joint committee on sports.