The men, who have sought asylum in Greece, arrived by military helicopter on Saturday after sending a distress signal to authorities at the airport in the northern city of Alexandroupolis.
She added that they remained under arrest and had not made contact with their families.
The asylum seekers insist they took no part in the putsch and fled to Greece to save their lives “when policemen started shooting against them”.
Marinaki added that the soldiers — all married and in their forties — feared for the safety of themselves and their families.
Turkey’s Foreign Minister Mevlut Cavusoglu said Ankara had asked Athens to send the officers, including two majors, back following Friday night’s challenge to President Recep Tayyip Erdogan’s rule by discontented soldiers in which more than 250 people died.
Erdogan spoke late on Saturday by phone with the Greek Prime Minister Alexis Tsipras and thanked him for his stance during the failed uprising, according to Greek government sources.
Tsipras had early Saturday expressed his “support for the democratically elected” Turkish government.
According to Athens News Agency, the Greek Prime Minister told Erdogan that the procedure for the Turkish asylum seekers will be swift but in line with international law and human rights treaties.
Greek government sources estimate that the procedure will take up to two weeks. Early Sunday, the Blackhawk helicopter the asylum seekers had used was flown back to Turkey.