Turkey's insistence in forging ahead with a contentious Mediterranean gas exploration plan is really over regional prestige, Greek analysts said Tuesday as a Turkish vessel began a second day of searches.

The row flared Monday when Ankara sent the research ship Oruc Reis near the Greek island of Kastellorizo, whose maritime rights Turkey disputes.

Marine tracking on Tuesday located the vessel southeast of the island of Crete. It is escorted by a Turkish navy flotilla and shadowed by Greek warships.

"Nobody believes that (Turkish President Recep Tayyip) Erdogan has sent the ship in this area to look for hydrocarbons. He is interested in showing the flag, (to make) a political statement," Constantinos Filis, executive director of the Institute of international Relations, told Greek news website Liberal.

"Turkey wants to show it is the dominant power in the Eastern Mediterranean," Angelos Syrigos, an international law professor who is now a government lawmaker, told Skai TV.

Turkey has announced the vessel would be carrying out activities between August 10 and 23.

The area is close to Turkey but belongs to Greece under international maritime law.

Turkey says the rules are unfair since Greece only has rights to the waters because of a few tiny islands that expand its legal reach.

Filis noted it was "impossible" for the ship to actually conduct seismic research with the noise of nearby warships.

And exploration "requires two months, not two weeks," he said.

Energy exploration in the gas-rich eastern Mediterranean is a frequent source of tension between Turkey and a bloc of its neighbours including Greece, Cyprus, and Israel.

Greek Prime Minister Kyriakos Mitsotakis on Monday conferred with his military chiefs, and spoke with EU Council President Charles Michel and NATO Secretary General Jens Stoltenberg.

The Greek PM on Tuesday will brief other party leaders on the situation by phone.

Erdogan sounded a slightly more conciliatory note after a meeting with his own ministers later Monday.

"Let us all come together as Mediterranean countries and find a formula that protects all of our rights," Erdogan said in a national address.

But Erdogan added: "We cannot allow (nations) to ignore a big country like Turkey and try to imprison us to our shores."

Filis called the EU's response to the row "disappointing".

"European institutions are completely voiceless," he said.

The move came just days after the NATO allies seemed close to holding talks over disputed maritime zones in the Aegean.

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.