Turkish President Recep Tayyip Erdogan has given controversial speeches recently to mark the 100th anniversary of Turkey's victory in a three-year war against Greece that completed the creation of the post-Ottoman state.

He has repeatedly accused NATO ally Greece of "occupying" Aegean islands whose status was settled in post-war treaties and has warned that Turkey's armed forces could "come overnight" and "do what is necessary".

The letters, dated September 5 but published by EU member Greece Wednesday, said Erdogan's statements were "openly threatening" and "unacceptable".

"These public statements by the Turkish President speak for themselves: they are unprovoked, unacceptable and an insult against Greece and the Greek people," the letters signed by Foreign Minister Nikos Dendias say.

Erdogan has increased his verbal attacks on Greece ahead of next year's election that is expected to be his most difficult after 20 years in power.

"If you go too far, the price will be heavy," Erdogan said Saturday, referencing the 1922 fall of the western city of Izmir that was followed by its burning and a massacre of the ethnic Greek population.

In response to Turkey's claim that Greek islands have been illegally militarised, Athens counters that Turkey has a large fleet and army stationed on the coast facing the islands, and invaded Cyprus in 1974.

Dendias said Tuesday that statements by Turkish officials were growing "increasingly outrageous and unacceptable" and warned Greece's military "was adequate to defend our homeland".

The two uneasy neighbours have for years feuded over maritime borders and energy exploration rights in disputed parts of the Aegean, which separates the two countries, and in the eastern Mediterranean.

Athens also accuses Ankara of flying over Greek islands, while Turkey has been angered by recent Greek defence agreements with France and the United States.