Turkey's President Recep Tayyip Erdogan
His remarks come just hours after Athens said it would launch military exercises Wednesday with France, Italy and Cyprus in the region, where tensions between the two neighbours have escalated in recent weeks.
"In the Mediterranean, Aegean and Black Sea, Turkey will get what is rightfully ours," Erdogan said in the eastern province of Mus on the anniversary of the 1071 Battle of Malazgirt where pre-Ottoman tribes defeated the Byzantines.
The victory has been celebrated with increasing fervour in modern Turkey in recent years, and this year was no different with a socially-distanced audience listening to Erdogan.
"We don't have our eye on someone else's territory, sovereignty and interests, but we will make no concessions on that which is ours," he said in the televised speech.
"We invite our counterparts to change their ways and avoid wrongs that will be the path to ruin," Erdogan added in pointed remarks to NATO ally Greece.
"We want everyone to see Turkey is no longer a country whose patience, determination, means and courage will be tested. If we say we will do something, we will do it, and we will pay the price," he said.
Greece and Turkey are already divided on significant issues including migration and Byzantine heritage in Istanbul, formerly Constantinople.
But the discovery of hydrocarbon reserves in the eastern Mediterranean has further strained relations, with Turkey rejecting calls from the EU and Athens to immediately stop energy exploration in the region.
Turkey sent the Oruc Reis research vessel accompanied by warships to disputed waters on August 10. Its activities were meant to end on last Sunday but were extended to Thursday.
Germany has led the charge in Europe to defuse tensions, dispatching its foreign minister to Ankara and Athens on Tuesday to resolve the issue through dialogue.
Both sides said they were open to dialogue after talks with the German minister, and there will be an informal EU foreign ministers' meeting in Berlin on Thursday and Friday.