A Greek navy statement says the Turkish-flagged Karmate put on speed and made off into Turkish waters after Friday's pre-dawn incident, ignoring radio messages from the Armatolos gunboat to stop.
The navy said the collision in Greek waters southeast of the island of Lesbos was caused by the Turkish ship breaching international shipping safety rules.
Thr 180-foot (55-meter) Armatolos was taking part in a NATO operation to stop migrant-smuggling, the navy said.
Turkey's Transportation, Maritime and Communication Ministry said coordination between Turkish and Greek search and rescue centers was established following the incident.
The incident comes amid heightened tension between Greece and Turkey over Aegean territorial rights.
