Turkish Foreign Minister Mevlut Cavusoglu earlier said the docking of Turkey's Oruc Reis seismic survey vessel for maintenance does not mean its operations in the eastern Mediterranean are done.
Allies of the two North Atlantic Treaty Organisation members have warned that the standoff and rival military build-ups in the area - between Greek islands, Turkey's southern coast, and Cyprus - had increased the risk of a military confrontation.
The discussions, Petsas said, were taking place between aides to Greek Prime Minister Kyriakos Mitsotakis and Turkish President Recep Tayyip Erdogan.
The Turkish presidency said Erdogan told Merkel the dispute "could be resolved through negotiations. provided that a constructive approach, based on fairness, prevails".
"We can meet if there is goodwill".
It is expected that at a European Union leaders meeting on September 24-25, a decision will be made to sanction Turkey for its defiance of worldwide law and its threats of war against Greece and Cyprus.
"The recent withdrawal of the research vessel Oruç Reis is an important step paving the way for a meaningful dialogue between Greece and Turkey", said Stano.
The standoff appeared to be cooling off when Turkey's Oruc Reis research vessel and its accompanying fleet of warships ended their month-long mission in the area and pulled back to shore last weekend.
Dialogue with Ankara is still possible to de-escalate tensions in the Eastern Mediterranean, the Cypriot president said on Wednesday.
Ankara's dispute with Athens has sparked a crisis that has drawn in some European Union member states, particularly France which sent vessels and fighter jets to the region in support of Greece.
The EU says it fully supports member states Greece and Cyprus in their dispute with Turkey and has said unless the country shows "sincere cooperation and concrete progress" in easing tensions with Greece and Cyprus, there will be sanctions.
The Turkish navy on Tuesday also announced the extension of the Yavuz drillship's stay in disputed waters near Cyprus until October 12. Cyprus was split after a 1974 Turkish invasion spurred by a brief coup engineered by the military in Greece.
This government has always been at loggerheads with Turkey, which began drilling for oil and gas near Cyprus past year.
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