While Turkey tries to position itself on the global stage as a knowing mediator between Russia and Ukraine, albeit with questionable success, it is at the same time ratcheting up bellicose rhetoric directed at Greece, a neighbor and fellow NATO member. That one-sided war of words escalated today when a representative of the Turkish president’s Justice and Development Party issued a thinly veiled threat to invade Greece. 

The party official, Ömer Çelik, tweeted a series of photos from an ongoing Turkish military exercise under the words, “We may suddenly come one night.” Reactions in the Greek press left no doubt as to which country he meant.

One of the objectives of Turkey’s “EFES 2022” exercise is to sharpen the Turkish army’s ability to make a military landing on an island, which in practice could mean any number of Greece’s islands in the eastern Aegean Sea that face the Turkish western Mediterranean littoral. Mr. Çelik’s unneighborly tweet was accompanied by photos that appeared to depict Turkish army helicopters carrying artillery in a coastal direction, Turkish navy commanders destroying radar equipment with rockets, and artillery shells being destroyed.

What makes the threat significant is that President Erdogan has joined the fray. Observing the military exercise from Izmir, the Turkish leader said, “Once again, we call on Greece to stop arming the islands that have non-military status and to act in accordance with international agreements,” adding: “I’m not kidding, I’m serious. This nation is determined, if it says something, it will do it.”

Mr. Erdogan wants all of Greece’s islands in the Aegean Sea to be demilitarized. The use of the phrase “non-military status” is a reference to his party’s position that by having any kind of military installation on Greek islands, however minimal or perfunctory it may be, it puts Greece in contested observance of the Treaty of Lausanne. By that multipronged 1923 treaty, Turkey formally ceded all claims to Greece’s Dodecanese Islands,which include large islands such as Rhodes as well as smaller ones like Kastellorizo, which is only one mile from the Turkish coast. 

Because the Aegean islands to which Mr. Erdogan is referring are all Greek, making Greece free to do whatever it wants on its sovereign territory, his remarks are perceived at Athens as more than just a taunt. He also called on Athens to “not to repeat the mistakes it made a century ago.”

The Athenian newspaper Kathimerini, closely aligned with the center-right New Democracy party of Prime Minister Mitsotakis, said Greece maintains that Turkey is deliberately misinterpreting the treaties regarding armed forces on its eastern islands and says it has legal grounds to defend itself following hostile actions by Ankara, including what appears to be a renewed threat of war if it extends its territorial waters.

On Thursday, the Greek Ministry of Foreign Affairs responded to the spate of recent Turkish claims about the status of the sovereignty of the Aegean islands by publishing 16 maps with the aim of demonstrating “in a vivid and irrefutable way the illegal and unilateral Turkish actions and claims.”

While Mr. Erdogan has in recent weeks publicly written off any kind of dialogue with Mr. Mitsotakis, it is likely that the two leaders will face off at a NATO summit scheduled to take place in Spain June 28-30. Depending on how choppy the sometimes deceptively calm waters of the Mediterranean get before that, the men will have either very much to discuss at Madrid — or very little.

Correction: The 1923 Treaty of Lausanne is at issue between Turkey and Greece. An incorrect treaty from another year was referenced in an earlier version of this article.