Turkey and Greece have agreed to talks over disputed waters in the eastern Mediterranean, both sides said on Tuesday, after German-led efforts to defuse a crisis that has raised fears of conflict.

A standoff over gas exploration in contested waters has seen the NATO neighbours stage rival war games and ramp up their rhetoric, but the tone has softened this week, raising hopes for a diplomatic solution.

The latest flare-up began in August when Turkey sent a research vessel accompanied by warships to disputed waters near a Greek island, and prolonged the mission three times despite repeated calls from the European Union and Greece to stop.

But both sides said on Tuesday they were "ready to start exploratory talks" as a three-way videoconference between Turkish President Recep Tayyip Erdogan, German Chancellor Angela Merkel and European Council chief Charles Michel took place, the Turkish presidency said.

The Greek foreign ministry also confirmed the talks, saying they would be held soon in Istanbul, without providing any precise date.

EU migration crisis
Germany has mediated between the two neighbours to ease tensions. Photo: TURKISH DEFENCE MINISTRY / -

Greece and Turkey have held talks on continental shelf disputes before -- the last were in 2016.

Ankara argues that it has the largest coastline of all the eastern Mediterranean nations but a disproportionately small share of the sea because of Greece's far-flung islands -- some of them within sight of Turkey's shore.

Athens says its claims are grounded in international law and past agreements signed by Ankara.

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Erdogan spoke to the United National General Assembly Photo: UNITED NATIONS / Rick BAJORNAS

Turkish officials have insisted the Oruc Reis will return to its work, and ship-tracking website marinetraffic.com showed that the ship was on the move on Tuesday afternoon -- although it was not clear where it was heading.

Turkey has also extended the mission of another research vessel in disputed waters off Cyprus until October 18. A drill ship will also remain off Cyprus until October 12.

Greece and France have both demanded tough sanctions against Ankara, which could be agreed at an EU summit on October 1 and 2.

Erdogan and French President Emmanuel Macron have traded barbs for weeks over the issue -- Turkey accusing the French leader of arrogance and despair after he called for a tough EU stance.

France also angered Turkey by sending fighter jets and vessels to the region in support of Greece.

However, the two men spoke over the phone late on Tuesday in their first contact since the tensions flared.

French officials said Macron told his counterpart to avoid taking any action likely to raise tension and to "engage without ambiguity in the construction of an area of peace and cooperation in the Mediterranean".

The Turkish side said Erdogan told Macron he expected "common sense and a constructive attitude" from France, claiming that he supports dialogue and cooperation to solve problems.

In an address to the United Nations General Assembly via videoconference earlier, the Turkish leader called for "sincere dialogue" to settle the row and rejected "any imposition, harassment, or attack in the opposite direction".

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