“Erdogan is a little bit out of control — he’s picking a lot of fights and there is a lot of uncertainty about how far he’s prepared to go,” said Nikos Tsafos, who researches the politics of the Eastern Mediterranean at the Center for Strategic and International Studies, a Washington-based think tank.

“The odds of something going wrong are increasing on a weekly basis,” he said.

The border issue has its roots in the collapse of the Ottoman Empire in the aftermath of World War I, and in subsequent international treaties that gave many islands that had once belonged to the Ottoman Empire — including Kastellorizo, the nearest permanently inhabited island to Ro — to other European powers.

Today, Turkey — which was formed from the rump of the Ottoman Empire — does not contest Kastellorizo’s sovereignty. But the government feels it is unfair that Greece should have the right to potentially exploit energy resources in parts of the Mediterranean seabed that lie within sight of Turkey but many hundreds of miles from the Greek mainland.

“At the fundamental level, there is a different perception of how the Aegean Sea should be treated,” Mr. Tsafos said.

Other recent developments have compounded the decades-old disagreement. Talks have broken down over the status of the island of Cyprus, which is divided between a Greek-backed and internationally recognized state in the south, and a Turkish-backed breakaway state in the north.

Greece declined to extradite eight Turkish servicemen who had fled following a failed coup in 2016; and the Turkish government has arrested two Greek border guards, seemingly in response.