The Turkish-flagged drillship Fatih launched offshore drilling operations this May in an area 75 kilometers (42 nautical miles) off the western coast of the island of Cyprus.
On Wednesday, the foreign ministry said Turkey's Fatih ship had started drilling activities to the west of the Mediterranean island at the start of May and its Yavuz ship had recently arrived east of Cyprus and would also conduct drilling activities.
"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.
The ministry stressed that Cyprus' membership in the European Union did not mean that the island's Greek community could "usurp the legal rights and interests of Turkish Cypriots".
The second Turkish vessel, "Yavuz, ' has sailed to an area off the Karpas peninsula on Cyprus" east coast.
There has been no comment so far from Turkey which sent a drilling ship to the Mediterranean off Cyprus Monday, sparking a protest by the Greek Cypriots.
The Greek south has global recognition while only Turkey recognizes the government in the north.
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. Cyprus says Turkey is encroaching in waters where the country has exclusive economic rights while the European Union warned Turkey of sanctions. "We urge Turkish authorities to halt these operations and encourage all parties to act with restraint and refrain from actions that increase tensions in the region", a U.S. State Department spokeswoman said in a statement.
The statement came in response to a comment by Greek Foreign Minister Nikos Dendias that "Turkey should stop being the spoiled child of the Eastern Mediterranean" amid escalating tensions over the oil and gas resources on seabed.