* Turkey and Cyprus have overlapping claims in Mediterranean
* EU leaders issue statement warning of action (Adds EU statement)
DILOVASI, Turkey/BRUSSELS, June 20 (Reuters) - Turkey launched a second drilling ship on Thursday which will conduct natural gas operations off the northeast coast of Cyprus for three months, a move which risks aggravating a conflict with Cyprus over jurisdiction rights for oil and gas exploration.
Turkey and the internationally-recognized government of Cyprus have overlapping claims in that part of the Mediterranean, an area thought to be rich in natural gas.
Energy Minister Fatih Donmez said at the launch of the vessel, Yavuz, it would operate in a borehole near Cyprus' Karpas Peninsula, and reach a depth of 3,300 meters (3,609 yards).
Turkey already has a ship offshore Cyprus, and Cyprus last week issued arrest warrants for its crew.
European Union leaders warned Turkey on Thursday to end its gas drilling in disputed waters or face action from the bloc, after Greece and Cyprus pressed other EU states to speak out.
At an EU summit in Brussels, leaders issued a formal statement saying Turkey's drilling is "illegal" and that the bloc "stands ready to respond appropriately."
"The European Council underlines the serious immediate negative impact that such illegal actions have across the range of EU-Turkey relations," leaders said, using the official title of their summit. "The European Council calls on Turkey to show restraint."
The statement also threatened "targeted measures": EU code for possible travel bans and asset freezes of Turkish companies and individuals involved in the drilling.
The dispute has escalated in the past month and also risks straining Ankara's relations with its western allies.
Ankara, which does not have diplomatic relations with Cyprus, claims that certain areas in Cyprus's offshore maritime zone, known as an EEZ, fall under the jurisdiction of Turkey or of Turkish Cypriots, who have their own breakaway state in the north of the island recognized only by Turkey.
Cyprus says that defining its EEZ is its sovereign right.
Donmez said unilateral agreements made between Cyprus and the regional countries that attempted to "steal" the rights of Turkey and Turkish Cypriots had "no legal validity."
"Turkey will continue its operations in its own continental shelf and in areas where the Turkish Republic of Northern Cyprus has licensed Turkiye Petrolleri without stopping," Donmez said, referring to Turkey's main oil exploration company.
"We are warning actors from outside the region that are forming cooperations with Cyprus: Do not chase illusions that will yield no results," he said.
The bloc will now ask its foreign service, the European External Action Service, to put forward options, the statement said.
Cyprus has threatened to jeopardize the EU membership bids of North Macedonia and Albania if the bloc does not take action against Ankara.
One senior EU official said that, aside from sanctions, one option was to end talks with Turkey over extending a customs union, which already allows tariff-free trade with the EU for industrial goods but not services or agriculture.
Another option could be formally suspending Turkey's status as an official candidate to become a member of the European Union, although talks have been frozen for over a year.
Cyprus was divided in 1974 after a Turkish invasion triggered by a brief Greek-inspired coup. Several peacemaking endeavors have failed and the discovery of offshore resources has increasingly complicated peace negotiations. (Reporting by Can Sezer and Ezgi Erkoyun in Dilovasi and Robin Emmott in Brussels; writing by Ali Kucukgocmen and Tuvan Gumrukcu; editing by Daren Butlers, Alexandra Hudson and Jonathan Oatis)