Turkey on Thursday announced new naval exercises near its shores and accused France of "bullying" as the conflict over Mediterranean energy riches risked turning into a military standoff. 

The Turkish navy said it would stage "gunnery exercises" at the edge of its territorial waters in the northeastern corner of the Mediterranean Sea next Tuesday and Wednesday.

Defence Minister Hulusi Akar said the drills were "security related" and did not directly concern Turkey's controversial search for natural gas that has pitted it against Greece and the EU.

The two NATO members have been staging rival war games in a conflict that could imperil Europe's access to vast new energy deposits and further destabilise war-torn Libya and parts of the Middle East.

US President Donald Trump spoke to Greek Prime Minister Kyriakos Mitsotakis and Turkish President Recep Tayyip Erdogan on Wednesday -- his first direct involvement in the escalating dispute.

The Turkish defence minister did not say whether the Oruc Reis research vessel and its accompanying navy frigates would leave waters claimed by Greece on Thursday as planned.

But he warned: "There's neither a deadline nor a limit" to Turkish exercises and exploration in the eastern Mediterranean. They will be carried out as much as they are needed ... We are determined to protect our rights."

Trump gets involved 

Germany's intensifying efforts to calm the rhetoric and get talks on track have so far been ineffective. EU foreign ministers will tackle the crisis in Berlin on Thursday and Trump took the pulse of both sides through his own round of telephone diplomacy.

The White House said Trump "expressed concern over increased tension between NATO allies Greece and Turkey".

Greek Prime Minister Kyriakos Mitsotakis said afterwords that Athens was "ready for a significant de-escalation -- but on condition that Turkey immediately stops its provocative actions".

Erdogan has already rejected agreeing to preconditions before talking to Greece. The Turkish presidency said Erdogan "reminded (Trump) our country was not the one creating instability in the eastern Mediterranean".

Erdogan "emphasised how Turkey has taken concrete steps which proves it sides with lowering tensions and dialogue," the presidency said.

Greece's European support is led by EU military powerhouse France. French frigates and fighter jets joined the Greek war games -- also including Italy and Crete -- on Wednesday while Turkey staged smaller ones nearby with a US navy ship.

The French intervention has particularly upset Turkey. "The time for bullying is over. You have no chance to force (us) to take some actions through bullying," Akar told France in a televised interview. "It's an empty dream to think about preventing or changing the activities of Turkey or the Turkish armed forces," he said of the French military presence in the region.

Akar also urged Greece to stop hiding behind France or the EU and said: "As Turkey and the Greeks, we need to solve our problems by holding talks... We say we should talk, we say dialogue and want a solution."

The EU meanwhile appears divided over how to respond. Greece's push to sanction Turkey failed to get off the ground at an EU foreign ministers' video conference on August 14.

Turkey's position found some support from southern European countries that would be most directly affected should Erdogan retaliate against the bloc. Greece is expected to try again at the EU meeting in Berlin on Thursday and Friday.