In an official statement on Tuesday, the Turkish foreign ministry stated the bloc's moves "will not affect in the slightest our country's determination to continue hydrocarbon activities in the Eastern Mediterranean".
"If [Brussels] takes such decisions against Turkey, we will increase activities [in the Eastern Mediterranean]".
The European Council published a final declaration Monday following a meeting of the EU's Foreign Affairs Council attended by foreign ministers of member states.
Regardless of warnings by the European Union and the United States to stop its drilling activities near Cyprus' coasts, Ankara has sent two drilling vessels, Fatih and Yavuz, to the Eastern Mediterranean for oil and gas exploration.
"A very pragmatic position would be that negotiations need to restart now", Tzimitras told Al-Monitor, adding they could facilitate "de-escalation and a platform for the two sides on the island to discuss their positions", which could be expanded to energy cooperation issues, as well as Turkey's ongoing drilling activities.
"This is a game of brinkmanship, a game of chicken with Turkey saying, 'I can stand whatever sanctions you send my way, but I'm going to keep on drilling and you can't stop me.' And then the question is who will blink first".
Drilling started in 2018, and the partners announced a major discovery in March 2019, with preliminary findings suggesting approximately 5 to 8 trillion cubic feet of gas reserves.
"We have three ships there, God willing we will send a fourth ship to the eastern Mediterranean as soon as possible".
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Old tensions in the Eastern Mediterranean between Turkey and the European Union member state Cyprus about jurisdiction for offshore oil and gas deposits intensified after Turkey's decision to send a second drilling ship into disputed waters off the coast of Cyprus.
Cyprus has been divided since 1974 after Turkish troops entered the island under the claim of protecting Cypriot Turks from the Greek community. "Let them understand that they can not deal with Turkey with such methods", he added. Last week, diplomats began discussing what measures to impose.
Turkey has no diplomatic relations with the internationally recognized Cypriot government and is the only country which recognizes the breakaway state in the north of the island.
The EU ministers called on Turkey to respect Cyprus' sovereign rights in line with worldwide law and emphasized the "serious immediate negative impact" that Turkey's illegal actions were having on EU-Turkey relations. A second drilling ship, Yavuz, arrived off the northeastern coast earlier this month.
The EU also cut 145.8 million euros ($164 million) in pre-accession financial funds allocated for 2020.
The EU had been due to give Turkey 4.45 billion euros between 2014 and 2020, but it cut and suspended some funding past year.