Turkey's hunt for gas and oil reserves in waters claimed by Greece has put huge strain on the relationship between the two NATO members.

Turkish President Recep Tayyip Erdogan on Saturday raised the stakes and warned Greece: "They will either understand the language of politics and diplomacy, or on the field through bitter experiences."

NATO said earlier technical talks would start to avoid incidents between the two countries' navies, but Athens said it had not agreed to the talks and Ankara accused Greece of shunning dialogue.

As the tension ran high, the Turkish military began its exercises called "Mediterranean Storm" with the Turkish Cypriot Security Command, Vice President Fuat Oktay said on Twitter.

"The security priorities of our country and the TRNC (Turkish Republic of Northern Cyprus) are indispensable," Oktay said.

The Turkish defence ministry also tweeted that the exercises, which are due to last until Thursday, continued "successfully".

Cyprus is divided between the Greek Cypriot-run south -- an EU member state -- and the Turkish Cypriot north.

Turkey has stationed tens of thousands of troops in the north of the island since its 1974 invasion, which followed a coup engineered by military rulers in Athens.