Speaking to reporters in Madrid during a NATO summit, Kyriakos Mitsotakis said Greece intended to buy a squadron of the Lockheed Martin-made F-35s, with a possible option for a second squadron.
"Part of this procedure is the sending of the Letter of Request, which has occurred in recent days,'' Mitsotakis said, stressing this was the start of a lengthy process and that Athens estimated it would not take delivery of the aircraft before 2027 or 2028.
Greek officials said one squadron would consist of 20 planes.
Greece has already ordered 24 French-made Rafale fighter jets - six new and 18 previously in service with the French Air Force, as well as three French frigates.
Neighbors and NATO allies Greece and Turkey have long-running disputes over a series of issues, including territorial claims in the Aegean Sea and energy exploration rights in the eastern Mediterranean.
Recent quarrels have focused on the Greek islands off Turkey's coast, with Ankara accusing Athens maintaining a military presence on the islands in breach of treaties. Greece maintains it is acting according to international law and is defending the islands in the face of Turkish hostility.