"We express grave concern over Turkey's announced intention to carry out drilling activities within the exclusive economic zone of Cyprus", EU diplomatic chief Federica Mogherini has said in a statement.
Ankara's Fatih vessel entered Cyprus' exclusive economic zone in the west in May and has started drilling, while a second ship - the Yavuz - was deployed last month to search for oil and gas in the east.
"The drilling activities of our ship Yavuz are based on legal and legitimate grounds", the Turkish Foreign Ministry said in a statement, rejecting Greek and the EU's claims that the drilling activities are illegal.
Cyprus is divided between the internationally recognised Republic of Cyprus and a breakaway state set up after the 1974 Turkish occupation, following a coup sponsored by the military government then ruling Greece. Several peacemaking endeavors have failed and the discovery of offshore resources has increasingly complicated peace negotiations.
Cyprus has divided its EEZ off its southern coast into 13 blocks, or areas.
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The ministry said being a member of the European Union and "allegedly representing the entire Island" does not give the Greek Cypriot Administration the right to usurp the legitimate rights and interests of the Turkish Cypriots.
Reportedly the European External Action Service would also advise member states to refrain from high-level contacts with Turkey.
Israel and Egypt are among eastern Mediterranean countries that agreed this year to set up a forum to create a regional gas market and cut infrastructure costs.
It said Greece deserved the title of "Europe's spoiled child" and that European Union member Cyprus had together with Athens for years violated worldwide law and dragged the eastern Mediterranean towards instability.
"On their own, these measures. can not and will not stop the destabilising behaviour of Turkey in the eastern Mediterranean or more generally", he told Cyprus' Sigma TV.