Greece on Sept. 27 called on Turkey to condemn and investigate what it said was an "insult" to its national flag on the Greek island of Kastellorizo.
Greek media have reported that the blue and white Greek flag painted on a rocky hillside on Sept. 26 appeared stained with red paint. Kastellorizo is very close to the Turkish coast.
It was not immediately clear who was responsible for the incident.
"We blatantly condemn yesterday's insult of the Greek flag on Kastellorizo," the Greek foreign ministry said in a statement.
"We expect Turkish authorities to immediately condemn and investigate the incident, so that the culprits are brought before justice," it said. "Such unacceptable actions only seek to torpedo prospects for easing tensions between the two countries."
There was no immediate comment from Turkey.
Greek police were investigating, an official said. Greek media also reported that a drone equipped with a loudspeaker flew over Kastellorizo on Sept. 26, playing the Turkish national anthem.
Greece and Turkey disagree over a range of issues, including where their continental shelves extend. Tensions flared up last month after Turkey sent a seismic survey ship into disputed waters, escorted by gunboats, to map out sea territory for possible oil and gas drilling in an area thought to be rich in energy resources.
A Turkish and a Greek warship collided during the standoff. Since then, Turkey has recalled the Oruç Reis and the two countries have agreed to restart exploratory talks.