The French military said two Rafale jets would arrive Thursday on the island of Crete for a stay of "several days", after having taken part in a military exercise in Cyprus earlier in the week.
Relations between France and Turkey have been icy as President Emmanuel Macron has accused Ankara of violating the sovereignty of Greece and Cyprus - claims Turkey rejects.
Mr Macron told Greek Prime Minister Kyriakos Mitsotakis that the French military would monitor the situation.
"The risk of an accident lurks when so many naval forces gather in a limited area and responsibility in such a case will be borne by the one who causes these conditions", he said in a televised address.
North Atlantic Treaty Organisation allies Greece and Turkey vehemently disagree about their overlapping claims on hydrocarbon resources in the eastern Mediterranean based on conflicting views of how far their continental shelves extend in waters dotted with islands.
This handout photograph released by the Turkish Defence Ministry on August 12, 2020, shows Turkish seismic research vessel Oruc Reis (C) escorted by Turkish Naval ships in the Mediterranean Sea off Antalya on August 10, 2020.
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Earlier, Trump accused China of increasing the number of unemployed in the United States. Biden campaign spokesman Andrew Bates said Mr Trump is "easily threatened".
"We seek bridges of peace, good faith and cooperation with all", Mr Mitsotakis said, and expressed the hope that Turkey would come to the table for talks with goodwill on the one difference between the two countries, that of delineating the maritime zones in the Aegean and the East Mediterranean.
Turkey has said it plans to issue gas exploration and drilling licences in the region, somewhere between the Greek island of Crete and Cyprus, this month.
The French Defence Ministry said France's military presence "affirms the country's attachment to free movement, maritime safety and respect for global law in the Mediterranean Sea".
In apparent reference to France, Erdogan also said Greece was being pushed into taking "wrong steps" in the region by "a country that doesn't even have a coast in the eastern Mediterranean". "No provocation will. go unanswered".
Dendias is due to meet U.S. Secretary of State Mike Pompeo in Vienna on Friday.
Dendias said that during meetings with Prime Minister Benjamin Netanyahu and Foreign MInister Gabi Ashkenazi, he "made it clear that Turkey's illicit behaviour poses a threat to all countries in our region - a threat to security and stability".
Turkish Foreign Minister Mevlut Cavusoglu held calls with European Union foreign policy chief Josep Borrell and several European Union foreign ministers ahead of Friday's emergency meeting of the EU's Foreign Affairs Council that will discuss the situation in the eastern Mediterranean.