With tension escalating between the countries, Turkey on Feb. 3 said Greece violated international law by carrying out military exercises on the island of Kos, just off the Turkish coast.
The feud between the two NATO allies is growing daily with each side accusing the other of provocations and fears of an "accident," diplomatic code for military action.
The Turkish Foreign Ministry said Greek special forces had parachuted onto Kos in what Ankara claimed was a breach of a 1947 treaty that banned all such training on the island, the news agency Reuters reported.
Turkey accepts that treaty but rejects the 1923 Treaty of Lausanne that set borders between the countries as Turkish President Recep Tayyip Erdogan has openly coveted Greek islands near Turkey, including Kos.
A Greek defense ministry source confirmed there had been a scheduled exercise at the beginning of the week involving parachutists. "The training schedule of the Greek armed forces is not going to stop," the source told Reuters.
Turkey warned it could take action without specifying what that is. "We call on our neighbor Greece to refrain from unilateral actions that...could trigger tensions and are against international law," Foreign Ministry spokesman Huseyin Muftuoglu said in a statement.
Turkey cites laws it prefers for protection but routinely sends F-16 fighter jets to violate Greek air space and engage in mock dog fights with Greek jets and sends warships past Greek islands in violation of international laws it doesn't recognize.
Anxiety is rising in the wake of Greece's high court rejecting extradition of eight Turkish soldiers who fled a failed coup against Erdogan - they said they did not take part - and who landed a helicopter in Greece to seek asylum.
Greek Foreign Minister Nikos Kotzias told Greece's Alpha Radio that Turkey's behavior appeared to be an "attempt to externalize their internal crisis" and that it was important to keep calm and keep communications.
"We have made known to all allies and partners in NATO, our EU partners but also the United Nations, that Turkey may occasionally behave nervously, in a manner not becoming to the needs of normal development of bilateral relations," he said.
Kos is part of the Dodecanese chain of islands, placed under demilitarization as part of a peace accord after World War Two, when Italy ceded them to Greece.
Greece, which says Turkey was not party to that treaty because of its neutral stance in the war, started to militarize some islands after the Turkish invasion of Cyprus in 1974.