(Bloomberg) -- Turkey’s President Recep Tayyip Erdogan and Greece’s Prime Minister Kyriakos Mitsotakis agreed to intensify talks aimed at resolving longstanding regional conflicts that have strained relations between the rival nations on NATO’s southeastern flank.

The two leaders met Wednesday on the sidelines of the United Nations General Assembly in New York, their second bilateral in as many months, confirming a determination to follow a previously agreed road map for a series meetings through December to increase dialogue. 

Both leaders recently emerged from national elections, raising hopes that they might now have more political capital to offer compromises and improve relations. This comes at a time when Russia’s invasion of Ukraine is testing the North Atlantic Treaty Organization’s influence in the region. The two leaders confirmed their determination to maintain the positive atmosphere in relations, according to identical readouts issued after the meeting.

“We agreed to continue working to deepen the positive climate in Greek-Turkish relations,” Mitsotakis said in a statement. “At the same time, we had the opportunity to discuss a number of common challenges facing our two countries.”

Mitsotakis also said the two countries can increase cooperation against illegal migration. “I believe that Turkey’s cooperation is necessary in order to reduce immigration flows to a minimum,” he said.

Turkish and Greek foreign ministry officials are scheduled to meet in mid-October before debating confidence-building measures in November, according to the readouts, adding that a Greek-Turkish High-Level Cooperation Council meeting is scheduled to take place in Thessaloniki on Dec. 7. The council first met in 2010, and its most recent session was in 2016.

Turkey and Greece face a long list of disputes to solve, from defining maritime borders to the delineation of their airspaces. Another contentious issue is the future of Cyprus, where the leader of the local Turkish population is rejecting a call by the internationally recognized administration backed by Greece to restart talks to reunify the island as a bi-zonal federation.

The Conflicts That Keep Turkey and Greece at Odds: QuickTake

For Athens, the primary issue to resolve is defining the exclusive economic zones of the two countries in the Aegean and Mediterranean Seas. The dispute should be handled in international courts, but the two countries are nowhere near agreeing to that, Mitsotakis said Sunday. 

Turkey argues that pursuing a single dispute in court while leaving out others, such as disagreements over airspace and its demands for the demilitarization of some Greek islands, will result in failure. 

Erdogan will push for comprehensive talks with Greece, where all those bilateral issues can can be discussed simultaneously, senior Turkish officials familiar with the plans said. Turkey also wants negotiations over what it says is a Greek military buildup in the Aegean Sea and over the two countries’ continental shelves, the officials said, asking not to be identified because of the sensitivity of the matter.

Officials from both governments are preparing to take up some of those issues at the High-Level Cooperation Council gathering in Thessaloniki.

As an indication of the challenges Erdogan and Mitsotakis may face in bridging those gaps, the leader of Turkish-controlled northern Cyprus on Tuesday rejected restarting talks aimed at unifying the island unless the rival Greek Cypriot leadership in the south abandons its push for a federation to govern the entire country. 

Ersin Tatar, who echoes Erdogan’s views on Cyprus, said any future settlement for the divided island has to be based on the creation of two separate states, a notion flatly rejected by Greece’s foreign minister Georgios Gerapetritis.

Cyprus — less than half the size of New Jersey — was effectively partitioned in 1963 when fighting erupted between its two main groups: Greek and Turkish Cypriots. It was fully divided in 1974 after Turkey intervened, capturing the northern third of the island and saying it intended to protect the minority Turkish Cypriots following an Athens-backed coup by supporters of union with Greece.

--With assistance from Sotiris Nikas.

(Updates with remarks after meeting starting in fourth paragraph)

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