Tensions are running high over Turkey's drilling activities, which Greece and Cyprus say violate their sovereignty, and both sides have deployed warships in a show of force, raising fears of conflict erupting by accident.

The two NATO allies have now agreed to get together to discuss ways to avoid this, alliance chief Jens Stoltenberg said.

"Following my discussions with Greek and Turkish leaders, 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," he said in a statement.

"Greece and Turkey are valued allies, and NATO is an important platform for consultations on all issues that affect our shared security."

With the talks set to be of a technical military nature, they are unlikely to bring a complete solution to the complex, long-running rivalry between Greece and Turkey.

But observers will hope they will at least offer an opening for further dialogue.

The talks come after US Secretary of State Mike Pompeo urged the two sides to reduce tensions and open diplomatic channels to ease the crisis.

Turkish President Recep Tayyip Erdogan struck a defiant tone this week, extending the gas exploration mission and saying Ankara would not be intimidated by Greece's support from European military powers such as France.

The European Union has been watching the escalating row with growing concern, with Germany spearheading efforts to get the sides to temper the rhetoric and settle their differences through talks.

The EU has repeatedly urged Turkey to stop the exploration activities and threatened to slap sanctions on Ankara if it refused to solve the dispute through dialogue.