In what could be called the Asia Minor social media sensation that went major, an image of a large, framed map that depicts several major Greek islands — including the biggest one, Crete — as belonging to Turkey is making the rounds online. The revisionist map, apparently a present to the head of a nationalist party allied with Turkey’s president, Tayyip Erdogan, from a separate ultranationalist group, prompted an outcry from the Greek prime minister. 

“Take a good look at this map. Crete, Rhodes, Lesbos, Chios, Samos all consumed by Turkey,” the prime minister, Kyriakos Mitsotakis, tweeted on Monday. The Greek leader took his indignation one step further, adding, “Α fever dream of extremists or Turkey’s official policy? President Erdogan must make his position clear on his junior coalition partner’s latest antics.”

On Tuesday, Washington entered the fray between the two NATO-member countries with a long but notoriously fraught historical relationship. In response to a Greek media inquiry about the map, a state department representative said that “the sovereignty and territorial integrity of Greece is not in question,” adding: “We continue to encourage our NATO allies, Greece and Turkey, to work together to maintain peace and security in the region and … to avoid rhetoric and actions that could further escalate tension.”

If anything, Ankara has ratcheted up the tension. Soon after the map — which shows Turkey and the Greek islands coveted by the Turkish ultranationalists in matching red — went viral, the website of the Turkish news channel TR Haber published a report that claimed Greece illegally occupies three-fourths of Crete, the biggest of the Greek islands. The reported cited a former secretary general of the Turkish ministry of defense, Yumit Yalim, who made the claim based on revisionist interpretations of the 1913 Treaty of London, which was enacted following the end of the First Balkan War and the forced resignation of the Ottoman grand vizier, Kamil Pasha. 

Evoking the twilight years of the Ottoman Empire, Mr. Yalim said that while “it was expected that three-quarters of Crete would pass to its former owner, namely the Ottoman Empire, Athens created a de facto situation occupying the entire island.”

Ironically, the one-quarter of the elongated island of Crete that in the Turkish statesman’s claim actually does belong to Greece is the westernmost portion that happens to include Souda Bay, home to a major naval base serving both NATO and the Hellenic Navy. 

Staking out a claim to Souda Bay, even if just to generate buzz on the socials, is a line that so far no Turkish politician has crossed. A Greek newspaper, Protothema, noted that “it is known that due to its strategic position, Crete is an obstacle to the expansionist plans of Turkey” and the island functions as “a large aircraft carrier” that essentially controls the entire area of ​​the northeast Mediterranean Sea. 

Prior to the NATO summit last month at Madrid, Mr. Erdogan made repeated jabs at Athens because of its refusal to stop arming Greek islands in the Aegean Sea that have a special demilitarized status dating to the 1923 Treaty of Lausanne. Athens argues that Ankara is deliberately distorting iron-clad understandings regarding armed forces on the eastern Aegean islands and claims it has legal grounds to defend itself in the wake of hostile behavior by Ankara, including a long-standing threat of war should Greece extend its territorial waters from certain islands that are close to the Turkish coast. 

Bringing Crete into the war of words may not mean much on the ground right now, but it raises tensions. It also introduces a personal element into this rhetorical fracas. Messrs. Erdogan and Mitsotakis have a frosty relationship at best, and it did not thaw any at Madrid. While Mr. Mitsotakis is a son of Athens, he is also the scion of a prominent Greek political dynasty with roots in the Chania region of Crete, an island popular with vacationers this time of year but also one where Greek national pride runs deeper than the Mediterranean that surrounds it.