There was no sign of a Turkish naval escort for the Piri Reis and its 10 crew as the vessel set out, although Energy Minister Taner Yildiz had raised the possibility of such a security measure earlier this week.
Regional tension rose after Cyprus's Greek Cypriot government announced on Tuesday that drilling had begun in a southeast offshore area adjoining a gas field in Israeli waters reputed to be the world's largest find in the past decade.
Texas-based Noble Energy is carrying out the drilling in the Cypriot block. Speaking in New York on Thursday, Cypriot President Demetris Christofias said more blocks could be thrown open for exploration over the next 12 months.
Turkey contests an Cypriot-Israeli accord signed last year to create exclusive economic zones in the waters between them.
It also argues that Cyprus should not be exploiting natural resources until a settlement is reached between the Greek Cypriot government and a breakaway Turkish Cypriot state for the reunification of the island, and that any revenues should benefit both communities.
Christofias gave assurances this week that any money earned from a gas find would be used for the good of both sides regardless of whether a settlement had been reached.
Prime Minister Tayyip Erdogan touched on the dispute in an address to the U.N. General Assembly on Thursday.
"Turkey expects to see that all parties involved make efforts so that the Greek Cypriot administration ends initiatives that cause tension not only in the island but the region," he said. "Otherwise, we will do what we have to do."
In retaliation, Turkey and the Turkish Cypriot administration signed their own continental shelf agreement on Wednesday, permitting state-run Turkish Petroleum Corporation (TPAO) to start exploration north of the island.
And last week, Erdogan said Turkish warships could be sent to the eastern Mediterranean at any time and Israel could not do whatever it wants there.
Turkey's relations with Israel have soured in recent weeks after Israel refused to apologise following the release of a U.N. panel's report on the killing of nine Turks in an Israeli commando operation to stop an aid ship bound for Gaza, a Palestinian Islamist enclave under Israeli blockade, last year.
