Turkish Foreign Minister Ahmet Davutoglu met the Greek prime minister and foreign minister in Athens on Tuesday as part of ongoing efforts to sweeten relations between the two regional rivals and uneasy Nato allies.

Davutoglu's talks with his Greek counterpart Dimitris Droutsas and Prime Minister George Papandreou included the delineation of the Aegean Sea continental shelf, from the northern land border in Thrace to the southern Greek island of Kastellorizo, just off the Turkish coast.

"It is an honest, serious effort ... a real opportunity for our two countries," Droutsas told a press conference.

The issue, which will determine each neighbour's rights for exploration and exploitation of potential mineral and fossil-fuel deposits, has been among the most contentious in bilateral relations.

Greece and Turkey came close to war three times between 1974 and 1996 - once over a Turkish research vessel in the Aegean.

"We have crossed the threshold of psychological negativism and I think that is very important," Davutoglu said.

Relations have improved drastically over the past decade, despite tension over Cyprus, which remains forcibly divided between Greek and Turkish-speaking communities.

The two countries' cabinets held a joint meeting in Athens last year and Droutsas said a second such session will be held in Turkey in July.

Tuesday's talks included the current turmoil in Libya and Droutsas said both governments had agreed to intensify cooperation, particularly on humanitarian aid.

He said Greece backs Turkey's troubled bid for full European Union membership, "without half measures or special relationships," provided Ankara meets its commitments to the bloc and normalises relations with Cyprus.

"Our vision is to see Greece, Turkey and Cyprus (eventually) cooperating in Brussels for their common interests in the framework of an expanded Europe," Droutsas said.

After his meetings in Athens, Davutoglu is to travel on Wednesday to northeastern Greece, home to the country's 120,000-strong Muslim minority, which is based mainly in the region of Thrace.