Turkey has sent an energy exploration ship to search for gas and oil in waters off the Turkish-controlled north of Cyprus.
Turkey had warned it would take the step unless Greek Cypriots cancelled their own plans to drill for gas in waters they control to the south.
The Greek Cypriots insist they are fully entitled to explore for energy.
But Turkey argues that offshore natural resources belong to both communities on the divided island.
With Cyprus now a member of the EU, disputes over its sovereignty are a major obstacle to Turkey eventually joining the European bloc.
Live footage of the Piri Reis leaving the port of Izmir on Friday was broadcast on Turkish television.
There was no sign of a naval escort despite earlier suggestions by the Turkish government.
Regional tension rose after the Greek Cypriot government announced on Tuesday that drilling had begun in a south-east offshore area adjoining a gas field in Israeli waters.
The area is reputed to be the world's largest find in the past decade, Reuters news agency reports.
Texas-based Noble Energy is carrying out the drilling.
Turkish Prime Minister Tayyip Erdogan raised the dispute in a speech to the UN 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 the same forum, Cyprus President Demetris Christofias condemned Turkey's attitude.
"Turkish naval manoeuvres in the region... where exploration is being carried out are provocative and a real danger for further complications in the region," he said.