France on Thursday prepared to beef up its military presence in the Mediterranean as tensions rose, prompting Turkish President Recep Tayyip Erdogan to warn of a "heavy price" if a Turkish ship exploring for gas in disputed waters is attacked.

Tensions between Paris and Ankara increased with the latest French announcement linked to an escalating row in the eastern Mediterranean between Turkey and Greece over gas reserves.

France criticised its NATO ally Turkey over a drone strike this week in northern Iraq, while Erdogan accused French counterpart Emmanuel Macron of seeking to "bring back a colonialist structure" as he visited Lebanon after last week's catastrophic Beirut explosions.

The United States meanwhile called for a rapprochement, describing France and Turkey as "incredibly important NATO allies".

Existing rancour between uneasy NATO allies Turkey and Greece escalated when Ankara sent a seismic research ship named Oruc Reis to explore off the Greek island of Kastellorizo on Monday.

Turkey accompanied the Oruc Reis with several navy ships while its helicopters patrolled the surrounding skies.

Greece responded by sending its own military assets to the area to monitor Turkey's activities.

Erdogan appeared to suggest that the Oruc Reis had come under attack and that Ankara had responded accordingly.

"We told them, don't you dare attack our Oruc Reis. You will pay a heavy price if you attack our Oruc Reis, we said. And they got their first answer today," Erdogan said.

He provided no details and immediately moved on to another topic in his wide-ranging address.

The Greek defence ministry denied any involvement.

"No incident happened," a Greek defence official told AFP.

The two countries have been at loggerheads for months over Turkey's military intervention in Libya to support the UN-recognised Tripoli government, with France saying Turkey was bringing the NATO alliance's credibility into question.

France has also been critical of what it says are Turkey's violations of the sovereignty of Greece and Cyprus.

Erdogan seemed to suggest that the Turkish ship was attacked
Erdogan seemed to suggest that the Turkish ship was attacked TURKISH DEFENCE MINISTRY / Handout

This uneasy relationship was complicated further when Paris accused Turkish ships of being "extremely aggressive" towards a French navy vessel in June.

Ankara is at odds with Greece and the European Union over maritime rights in the Eastern Mediterranean over gas reserves.

The French defence ministry said two jets would arrive Thursday on the Greek island of Crete for a stay of "several days", and that French military vessels took part in joint exercises with the Greek navy overnight.

The moves were designed "to affirm France's commitment to free movement, to the security of maritime navigation in the Mediterranean and respect for international law", said a ministry statement.

Last month, Greece announced it had deployed ships in the Aegean in "heightened readiness" after Turkey announced plans for energy exploration near a Greek island in an area it claims is within Turkey's continental shelf.

Macron told Greek Prime Minister Kyriakos Mitsotakis on Wednesday that Turkey's "unilateral decisions" on gas exploration "must be stopped" to allow peaceful discussions within NATO, according to the French presidency.

Macron reiterated French and EU solidarity "for any member state whose sovereignty is challenged".

Erdogan meanwhile spoke to German Chancellor Angela Merkel and European Council President Charles Michel on Thursday about defusing the row with Greece.

Erdogan "stressed that he supported solving problems in the Eastern Mediterranean within the framework of international law and the principles of dialogue and equality", the presidency said.

But he criticised Macron for "putting on a show" with his visit to Beirut.

Macron was the first world leader to visit Beirut after the devastating explosions on August 4 which killed at least 171 people, wounded thousands more and left an estimated 300,000 homeless.

"Macron's concern is to bring back a colonialist structure," the Turkish leader said, referring to the years Lebanon spent under French mandate after the collapse of the Ottoman Empire.

On Thursday, the foreign ministry in Paris criticised a drone strike in northern Iraq that Baghdad labelled a "blatant Turkish drone attack" in its autonomous Kurdish region.

Iraq said the strike killed two of its high-ranking officers.