NATO allies Turkey and Greece are at loggerheads over energy riches, with overlapping maritime border claims and escalating tensions.

A Greek frigate collided with a Turkish one in August and the two NATO members staged rival war games in the energy-rich but disputed region last week.

Alliance chief Jens Stoltenberg has been trying to establish dialogue to avoid any future mishaps.

Stoltenberg on Thursday said Greek and Turkish leaders "agreed to enter into technical talks at NATO to establish mechanisms for military de-confliction to reduce the risk of incidents and accidents".

But Greece said later Thursday that Athens never agreed to the technical talks, saying Stoltenberg's statement did not "correspond to reality".

Turkish Foreign Minister Mevlut Cavusoglu said Greece did in fact agree to the proposal when it was made.

"Greece denied the secretary general's (remarks) but the one lying here is not the NATO secretary general, it's Greece itself," Cavusoglu told reporters in Ankara.

"Greece showed once more than it's not in favour of dialogue."

Greek Prime Minister Kyriakos Mitsotakis earlier on Friday said Turkey should drop "threats" against his country if talks on reducing tensions are to begin.

Greece and Cyprus claim Turkey's drilling activities in the eastern Mediterranean are a violation of their sovereignty.

Turkey deployed the Oruc Reis research vessel and warships to the disputed waters on August 10 and prolonged the mission three times, the latest until September 12.

The decision has also inflamed Turkey's ties with EU military powerhouse France.

French President Emmanuel Macron has called for Turkey to be sanctioned over its gas exploration and accused Ankara of treading on Greece and Cyprus' rights.

Cavusoglu took aim at Macron on Friday, accusing him of "hysteria".

"Who is supporting Greece? Who is provoking Greece the most? France. France has its own goals here. What is France's link to the eastern Mediterranean?

"My advice to France is this: this hysterical behaviour will benefit no one," calling on Paris to work with Ankara to solve issues including the eastern Mediterranean.