Greek Prime Minister Kyriakos Mitsotakis on Monday conferred with military chiefs after Turkey resumed oil and gas research near a Greek island, his office said.
A senior Greek minister added that navy ships were monitoring the Turkish seismic research ship Oruc Reis.
"We are in complete political and operational readiness," Minister of State George Gerapetritis said on state TV ERT.
"Most of the fleet is ready to be deployed wherever necessary," he said.
Turkish Energy Minister Fatih Donmez had earlier tweeted that the Oruc Reis had "reached the destination where work would be undertaken", near the island of Kastellorizo.
Mitsotakis' office said the PM had spoken to EU Council President Charles Michel on the issue, and would later speak to NATO Secretary General Jens Stoltenberg.
Energy exploration in the gas-rich eastern Mediterranean is a frequent source of tension between Turkey and a bloc of neighbours including Greece, Cyprus, and Israel.
Turkey sent out a message on NAVTEX, the international maritime navigational telex system, announcing the vessel would be carrying out activities off the island of Kastellorizo between August 10 and 23.
The move came just days after the NATO allies seemed close to talks over disputed maritime zones in the Aegean.
Turkey had called off an earlier search by the Oruc Reis last month to hold negotiations with Greece and Germany, which holds the rotating EU presidency.
But the mood soured last week after Greece and Egypt signed an agreement to set up an exclusive economic zone in the region.
The Turkish foreign ministry said the "so-called maritime deal" was "null and void".
Egypt, Cyprus and Greece have likewise denounced a contentious deal, including a security agreement, signed last year between Ankara and UN-recognised government in Libya.
Greece, Cyprus and Israel in January signed an agreement for a huge pipeline project to transport gas from the eastern Mediterranean to Europe despite Turkey's hostility to the deal.