The Turkish foreign ministry on Wednesday morning in a statement accused Brussels of not being able to "take on the role of impartial mediator" in the dispute.
Its Yavuz ship had recently arrived to the east of Cyprus and would conduct drilling activities.
Cyprus has been split between a Turkish Cypriot north and Greek Cypriot south since 1974 when Turkey sent troops to the island in response to a Greek military coup.
Meanwhile, the Greek Cypriots have signed EEZ agreements with Egypt, Lebanon and Israel to which Turkey has objected on the grounds, it says, that certain areas in Cyprus's EEZ, fall under the jurisdiction of Turkey or of the Turkish Republic of Cyprus.
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.
"This provocative step raises tensions in the region", the State Department said late Tuesday.
The Cypriot presidency on Monday accused Turkey of a "grave violation", and an European Union statement also rebuked the Turkish action.
Several peacemaking efforts have failed and the discovery of offshore resources in the eastern Mediterranean in the 2000s has complicated the negotiations.
The European Union said in a statement on Monday that a second attempt by Turkey to drill for oil and gas was an "unacceptable escalation", having already warned Ankara to stop its "illegal" activities or face sanctions.
Cypriot Foreign Minister Nikos Christodoulides said any measures were not an end in themselves, but aimed at sending specific messages to Turkey.
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