Greek seamen have accused Turkish sailors of trying "to kill" them after the latter's patrol boat apparently rammed their vessel in the Aegean.
Each side blamed the other for Monday's collision off an islet known as Imia in Greek and Kardak in Turkish.
Seeking worldwide support, Prime Minister Alexis Tsipras underlined that Greece's border was also that of the 28-nation European Union, and his foreign minister briefed the head of North Atlantic Treaty Organisation and the US military chief on Turkey's "provocative behavior".
"Greece is not a country which plays games".
The ramming incident comes as Turkish President Recep Tayyip Erdogan issued a warning on Tuesday (February 13) to Greece, Cyprus and worldwide companies exploring for gas in the eastern Mediterranean not to "step out of line" and encroach on Turkey's rights.
Turkey's Foreign Ministry denied the Turkish vessel was at fault.
In Brussels, Greek Defence Minister Panos Kammenos said he had briefed U.S. Defence Secretary Jim Mattis and North Atlantic Treaty Organisation chief Jens Stoltenberg.
Many in Turkey dispute Greek ownership of the Aegean islets near Turkey's coastline.
Yildirim said that the Aegean should be a sea of friendship and refrained from repeating the claim made by the Turkish Foreign Ministry on Tuesday that Imia belongs to Turkey - even though he blamed Monday's incident on Greek violations.Tensions on Cyprus however remain, as Turkish warships continued their naval blockade of Block 3 in the island's exclusive economic zone (EEZ).Moreover, Yildirim reportedly told Prime Minister Alexis Tsipras that Nicosia can not continue with hydrocarbon exploration without a solution to the Cyprus problem. "It has full responsibility".