Nato on Thursday said that Greece and Turkey had agreed to talks to ease their dispute over eastern Mediterranean borders and energy rights, but Athens swiftly denied any deal on negotiations.
Alliance chief Jens Stoltenberg said he had won the two neighbours' agreement to enter "technical talks" designed to avert an accident between their navies that could cause a broader conflict.
A Greek ship collided with a Turkish frigate in August and the two Nato members staged rival war games in the energy-rich region last week.
"The two allies have agreed to enter into technical talks at Nato to establish mechanisms for military de-confliction to reduce the risk of incidents and accidents in the Eastern Mediterranean," Mr Stoltenberg said.
"Greece and Turkey are valued allies, and Nato is an important platform for consultations on all issues that affect our shared security."
But later on Thursday, Greece denied it had agreed to hold Nato-brokered talks with Turkey.
"Published information claiming Greece and Turkey have agreed to hold so-called technical talks on de-escalating tensions in the eastern Mediterranean do not correspond to reality," its Foreign Ministry said.
"De-escalation will only take place with the immediate withdrawal of all Turkish vessels from the Greek continental shelf."
Ankara said it backed the idea of talks at Nato.
"This initiative is supported by our country," the Turkish Foreign Ministry said. "We expect Greece to support the Nato Secretary General's initiative."
Turkey stressed that the talks would only focus on avoiding accidents and not resolving differences over maritime borders and energy exploration rights.
But observers still hope the talks will create an opening for further negotiations in a conflict that threatens to impede Europe's future access to a wealth of natural gas reserves.
Nato's announcement came after US Secretary of State Mike Pompeo urged the sides to ease tension and open diplomatic channels to ease the crisis.
Turkish President Recep Tayyip Erdogan this week extended a gas exploration mission near a Greek island at the centre of the longstanding rivals' latest dispute.
Mr Erdogan on Tuesday vowed not to be intimidated by Greece's support from European military powers such as France.
The EU has been watching the row with growing unease.
Germany had been leading efforts to get the sides to temper their speech and settle their differences through talks.
The Turkish presidency said Mr Erdogan held video conference talks with German Chancellor Angela Merkel on Thursday, in which he condemned "the support given to Greece's selfish and unfair stance by some countries".
The EU threatened to put sanctions on Turkey if it refused to solve the dispute through dialogue.