Exercises sign of increased cooperation among countries that increasingly view Turkey as a rival in the Mediterranean.
Senior diplomats from Greece and Turkey have met in Athens in an effort to ease longstanding maritime disputes before a European Union summit later this month.
Diplomatic sources said another round of talks resumed in a central Athens hotel on Tuesday, however, no details were given on the substance of the meetings.
The two neighbouring NATO allies are at odds over issues such as competing claims over their respective continental shelves, maritime rights, and air space in the Mediterranean, energy, ethnically split Cyprus, and the status of some islands in the Aegean Sea.
Underlining the tensions, Turkey this week protested against a deal between Greece, Israel and Cyprus for an undersea cable linking their electricity grids.
According to the state-run Anadolu news agency, Ankara believes the planned route for the cable runs through Turkey’s continental shelf.
The exploratory talks are meant to lay the ground for formal negotiations, but the two countries have made little progress in more than 60 rounds of meetings since 2002 and cannot even agree on what issues to discuss.
Greek foreign minister Nikos Dendias said he was willing to meet his Turkish counterpart Mevlüt Çavuşoğlu but any meeting “must take place in the right atmosphere”.
Ending a five-year hiatus, officials met in January after months of tension in the eastern Mediterranean.
Athens has said it will discuss only the demarcation of exclusive economic zones and the continental shelf in the Aegean and eastern Mediterranean, not issues of “national sovereignty”.
Ankara, which hopes to improve its relations with the EU – which has supported EU-member Greece and threatened sanctions on Turkey – has said it wants all issues, including air space and the Aegean islands, on the table.
The deliberations are scheduled to end with political consultations between the two countries’ ambassadors on Wednesday.
European leaders are also expected to discuss the eastern Mediterranean at a meeting on March 25-26.
NATO chief Jens Stoltenberg expressed “serious concerns” over Turkey’s actions in comments to European legislators on Monday.
He cited not just Ankara’s claims in the eastern Mediterranean but also its decision to buy the Russian air defence system S-400 and its record on human rights at home.
Ankara, however, remains defiant.
In a video conference with military officers, Turkey’s defence minister Hulusi Akar called on Athens to abandon its “uncompromising and provocative attitudes”.
He denounced what he said were Greece’s efforts to drag the EU and the United States into what was essentially a bilateral dispute.
Greece, which in recent years has reached maritime accords with Italy and Egypt, argues if the two sides fail to agree they should refer the dispute to the International Court of Justice.