ATHENS — Greece's prime minister warmly thanked France Thursday for its decision to boost its military presence in the eastern Mediterranean, where Greek and Turkish warships are closely shadowing each other over a Turkish energy exploration bid in waters Athens claims as its own.

Meanwhile, Turkey accused Greece and Cyprus of encroaching on its rights in the Mediterranean and vowed to defend its interests in the region but also called for dialogue to resolve the dispute over energy rights.

Kyriakos Mitsotakis tweeted that French President Emmanuel Macron is "a true friend of Greece and also a fervent protector of European values and international law."

The mounting tension follows Turkey's move Monday to send a seismic research vessel, escorted by warships, into waters between the Greek island of Crete and Cyprus to prospect for potential offshore gas and oil reserves, following similar discoveries in other parts of the region.

Greece claims part of the area is over its own continental shelf and has demanded that the Turkish ships withdraw. Turkey counters that it's entitled to conduct research in the area. Greece placed its military on alert, and sent warships to the area off Turkey's southern coast.

In Ankara, Turkish President Recep Tayyip Erdogan reiterated a call for dialogue and said he would hold talks with German Chancellor Angela Merkel and European Council President Charles Michel later on Thursday to discuss the standoff.

"The path for a solution in the eastern Mediterranean is dialogue and negotiation," Erdogan said during an address to his ruling party's officials. "A formula based on a win-win solution that protects the rights of all can be found if we act with common sense and reason."

"Greece's attitude in the Aegean and the Mediterranean is malicious," Erdogan said, adding that the Greek island on which Athens bases its continental shelf rights is located just 2 kilometers (1.25 miles) from the Turkish coast and 580 kilometers (369 kilometers) from the Greek mainland.

Erdogan said: "We don't have designs on anyone's rights, but we won't let any country take away our rights."

The Turkish leader also accused France of "provoking" Greece and Cyprus into taking "wrongful steps."

The French defense ministry said two Rafale fighter jets are making a stop on Thursday at Souda, on Crete, after being previously deployed in Cyprus for an exercise. 

At sea, the French Lafayette frigate left Cyprus' port of Larnaca and took part in a maritime exercise with the Greek Navy, the statement said. The Lafayette overnight joined the French helicopter carrier Tonnerre, en route to help Lebanon following the devastating explosion in Beirut.

"That military presence is aiming at reinforcing France's autonomous assessment of the situation and affirms the country's attachment to free movement, maritime safety and respect for international law in the Mediterranean Sea," the ministry said.

Macron announced following a phone call with Mitsotakis late Wednesday that he has decided to "temporarily reinforce the French military presence in the Eastern Mediterranean in the coming days, in cooperation with European partners including Greece."

Greece's NATO and European Union ally France is the EU's biggest military power. Complicating matters, Turkey — Greece's historic regional rival — is also a NATO member but has poor relations with France.

In a televised statement Wednesday, Mitsotakis warned of the "risk of an accident" in the area where the Greek and Turkish warships are gathered.

"In such a case, responsibility lies upon the one who gives rise to these circumstances," he said. He added that Greece is not averse to "even the toughest dialogue," but that "dialogue becomes irrelevant in a climate of tension and provocation."

"We will never be the ones to escalate the situation. Yet, self-restraint is only one aspect of our power," Mitsotakis said. "No provocation will … go unanswered."

On Thursday, Greek Foreign Minister Nikos Dendias traveled to Israel for talks on the matter. Dendias is due to meet U.S. Secretary of State Mike Pompeo in Vienna on Friday.

Meanwhile, Turkish Foreign Minister Mevlut Cavusoglu held calls with EU foreign policy chief Josep Borrell as well as the foreign ministers of Bulgaria, Estonia, Finland, Italy, Hungary and Lithuania ahead of an emergency meeting of the EU's Foreign Affairs Council to discuss the situation in the eastern Mediterranean.