Greek Prime Minister Alexis Tsipras called Turkish Prime Minister Binali Yildirim late Sunday, confirming that the extradition process had begun, the ministry said in a statement.
Tsipras congratulated Turkish citizens and their government on efforts to render the attempted coup unsuccessful, acknowledging the "importance for the whole region of maintaining the constitutional democratic regime and stability in Turkey".
The Greek prime minister also reiterated the support of his government and people, the statement said.
Yildirim thanked Tsipras for the sensitivity and support of the Greek government in the process.
Turkish President Recep Tayyip Erdogan said Sunday that in a telephone conversation with Tsipras the previous night, the Greek leader told him that the Turkish officers would be returned within 10 to 15 days.
The Black Hawk helicopter used in the attempted escape was returned Saturday to Turkey.