The EU has threatened to impose sanctions on Turkey if it continues "illegal drilling" in waters near Cyprus in the eastern Mediterranean.
The warning came at an EU summit in Brussels. EU Commission President Jean-Claude Juncker called Turkey's actions "totally unacceptable".
Turkey launched a second drilling ship - the Yavuz - on Thursday for natural gas and oil prospecting off Cyprus.
The Republic of Cyprus is in the EU, but the breakaway north is pro-Turkey.
The European Council - the EU government leaders - called on Turkey to "show restraint, respect the sovereign rights of Cyprus and refrain from any such actions".
"The European Council endorses the invitation to the [EU] Commission and the EEAS [EU foreign affairs service] to submit options for appropriate measures without delay, including targeted measures," the statement said.
The self-declared Turkish Republic of Northern Cyprus is recognised only by Turkey, and is internationally isolated.
Turkey said it was drilling inside its continental shelf, complying with international law. Reuters news agency reported that a Turkish drilling ship, the Fatih, had been anchored west of Cyprus since early May and had begun drilling.
Turkey is a candidate for EU membership but its negotiations are currently frozen. The EU Commission has said President Recep Tayyip Erdogan's government has backtracked on pledges to improve justice and the rule of law. The government has purged state institutions since an abortive coup attempt against Mr Erdogan in July 2016.
Greek Prime Minister Alexis Tsipras said the threatened EU measures "are against companies and individuals, a possible EU accession process freeze and measures with significant economic consequences".
"These will take place unless Turkey stops its illegal operations inside the Exclusive Economic Zone of Cyprus," he said in Brussels.
Turkey - a key Nato partner for the West - has extensive trade ties with the EU and has not yet been hit with EU sanctions, unlike Russia.
The US has threatened Turkey with sanctions if Mr Erdogan goes ahead with a deal to buy S-400 air defence missiles from Russia.