Tuesday’s talks are taking place behind closed doors a day after Ankara sent a diplomatic note to Israel, Greece and the European Union asking them to seek permission before conducting work in Turkey’s continental shelf.
NATO members Greece and Turkey are meeting in Athens to try once more to settle their standoff over eastern Mediterranean borders and energy rights.
Tuesday's meeting follows one in Istanbul in January, the first direct talks between the two sides on the dispute in nearly five years.
But the discussion will also be the 62nd such meeting since 2000, a long series that so far has little to show for it.
Little has been released about the agenda for Tuesday's talks, which will take place behind closed doors.
Turkey's note to Israel, Greece, EU
Ankara ratcheted up the pressure a notch on Monday with a diplomatic note to Israel, Greece and the European Union.
It told them to seek its permission before assuming work on a proposed undersea power cable in eastern Mediterranean waters, Turkish state media reported.
Both sides cite a range of decades-old treaties and international agreements to support their conflicting territorial claims.
Turkey is furious that Athens is using its web of islands to lay claim to huge swathes of the Aegean and Mediterranean seas.
Turkey – the country with the longest coastline on the Mediterranean – sent out drillships to explore for energy on its continental shelf, asserting its rights in the region as well as those of Turkish Cypriots.
Greece makes its maritime territorial boundary claims based on small islands just kilometres off the Turkish coast.
To reduce tensions, Ankara has called for dialogue and negotiations to ensure fair sharing of the region's resources.
Athens told to end 'provocative attitudes'
Athens, so far, has only wanted to discuss the border around the Aegean, where some of its islands lie close to the Turkish mainland.
Ankara however insists that the talks should include setting out the exclusive economic zones and air space of the two states.
In a videoconference 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.
"They will not get anywhere like this," he said.