UPDATE 3-Greece urges Turkey to be calm on Cyprus drilling

* Greek, Turkish Cypriots at odds over drilling

* Erdogan to Greek PM: drilling should follow peace deal-official

* Turkish exploration ship off southern Cyprus--defence source (Adds Cypriot source on Turkish vessel off southern Cyprus)

By Lefteris Papadimas

ATHENS, Sept 26 (Reuters) - The Greek prime minister spoke to his Turkish counterpart on Monday, calling for calm in a dispute over gas exploration off Cyprus that has widened the island's Greek-Turkish divide and added to tension between Turkey and Israel.

Turkey, which backs a breakaway Turkish Cypriot state in northern Cyprus, has challenged the right of Cyprus and Israel to drill in an area believed to hold the world's biggest gas find of the past decade. Turkish Prime Minister Tayyip Erdogan last week called the drilling "madness".

Both Cyprus and Turkey had exploration vessels off southern Cyprus on Monday as the Greek and Turkish leaders discussed the situation, a day before peace talks on the divided island were set to resume.

"The prime minister said there should be self-restraint and calm," Greek government spokesman Ilias Mosialos told reporters after a phone conversation between George Papandreou and Erdogan.

"Unilateral actions that create problems in the region should be avoided", Mosialos quoted Papandreou as saying.

An official from Erdogan's office said Erdogan had told Papandreou it would be better if gas exploration and extraction took place after a peace settlement had been reached on the island, and said unilateral actions could harm negotiations.

The two discussed holding a high-level meeting on Cyprus, possibly between end-October and mid-November. They had been due to meet at last week's U.N. general assembly in New York but Papandreou stayed in Athens because of the debt crisis.

Greece, whose relations with fellow NATO member Turkey have warmed in the past decade after a long history of enmity, is not directly involved in the gas exploration. But it is a close ally of Greek Cyprus, a fellow European Union member and the divided island's internationally recognised authority.

PEACE TALKS

Tension rose after Cyprus announced last week that drilling had started offshore, close to 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.

Turkey responded by signing a deal with the Turkish Cypriot authorities in the north of the island to do likewise. Noble is also drilling off Israel and has announced major gas finds.

A Greek Cypriot defence source said a Turkish exploration vessel was sailing in international waters close to the Noble Energy gas rig off Cyprus on Monday.

The Piri Reis, which left the Aegean port of Izmir on Sept. 23, was about 50 miles away from the Noble Energy rig, south of the island, and between two other plots Cyprus has mapped out for future exploration, the source said.

Cyprus has 12 plots in all, but has given a concession to just one at the southernmost point of its maritime economic exploitation zone (EEZ).

The route of the Piri Reis suggested Ankara may not be restricting its surveys to waters off northern Cyprus. "... it's in international waters 50 miles northwest of the Cypriot plot," the source said.

Turkey does not recognise Cyprus and disputes its right to map out areas for oil and gas exploration, and to extract hydrocarbons until there is a peace settlement on the island.

The Greek Cypriot government, a signatory to the U.N. convention on the law of the sea which defines maritime boundaries for economic exploitation, says it has the sovereign right to explore for hydrocarbons.

Greek Cypriot leaders have said that revenues from any energy deposits could be shared with Turkish Cypriots even before a settlement of the conflict which divided the island along linguistic and religious lines in 1974.

(Additional reporting by Pinar Aydinli in Ankara and Michele Kambas in Nicosia; Writing by Ingrid Melander and Jonathon Burch; Editing by Tim Pearce)