Macron's office said in a statement, according to Reuters, that the French President expressed, in a phone call, with Greek Prime Minister Kyriakos Mitsotakis, his concern about unilateral Turkish drilling.
"Excavations must stop in order to allow for a peaceful dialogue between the two neighboring countries, which are members of NATO," he added.
The dispute escalated this week with the arrival of the Turkish seismic survey vessel Aruj Reis to a disputed area in the region, accompanied by warships.
"France will temporarily reinforce its military presence in order to monitor the situation in the region and demonstrate its determination to abide by international law," Macron's statement said.
Turkey and Greece are locked in a dispute over each other's entitlement to natural gas stocks, and the European Union member Cyprus' attempts to explore for gas in the eastern Mediterranean amid strong objections from Ankara.
Macron called last month for the imposition of European Union sanctions on Turkey over what he described as violations of the sovereignty of Greece and Cyprus over their respective territorial waters, and relations between Paris and Ankara are also tense due to the conflict in Libya.