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"It is now becoming more imperative than ever to face challenges and solve longstanding problems that divide us," Prime Minister Alexis Tsipras said on Monday shortly after his meeting with Turkish Prime Minister Binali Yildirim.

The implementation of our agenda must be based on good-neighbourly relations and mutual respect without actions that undermine them. The Aegean must be a sea of peace and stability, he noted.

He said their talks had covered all issues between Greece and Turkey - namely =relations between them, Turkey's relations with the EU, the Cyprus issue and developments in the region - as well as noting that their talks, "in addition to being honest and substantive, are also essential at this crucial time."

"We agreed that tensions should be prevented and not suppressed," Tsipras added, and therefore an open channel of communicaiton between armed forces chiefs in the two countries.

The positive agenda of the two countries is also developing in areas of strategic importance, such as energy, transport, counter-terrorism and the refugee - migration crisis, the Greek premier stressed.

In the field of Euro-Turkish relations, Greece supports Turkey's EU accession course, which can help resolve issues and stimulate further cooperation, added Tsipras.

The Greek Prime Minister expressed support for a solution on Cyprus that will ensure security for all the people of the island, without a need for third powers and always in line with the European acquis.

"Turkey's provocations and violations do not assist in a positive agenda," Tsipras said. "We are working so that 'Geneva 2' will be a step forward," he added in response to questions, announcing that the two sides agreed on closer cooperation and constant exchanges and preparation in the time left until the Geneva meeting on June 28, in order to achieve the best possible outcome.

Commenting on a statement by UN Special Advisor for Cyprus Espen Barth Eide that the June 28 meeting will be "the end of the road" for the Cyprus issue, Tsipras said that he did not adopt this view.

"I do not believe there is an end to the road. Instead there is our willingness to open a road, even when we are at a impasse. And this is the message that we two want to send via this meeting."

"I fully agree," added Yildirim, on his part, noting that "we must continue to open roads" and that Turkey "has the political will for the solution of this issue," if the other side was willing to find a way. At the same time, he noted that the Cyprus problem was not a UN issue but primarily concerned the Greek Cypriots and Turkish Cypriots.

"The solution must be fair and viable, and capable of putting an end to the problem. We, as prime ministers, will contribute in every possible and positive way so that the efforts of the two communities bear fruits," he added.

Tsipras also commenting on the extradition of eight Turkish military servicemen that fled Turkey after the failed coup and sought asylum in Greece. This was an issue that only Greek justice could decide, he said, and the rulings of Greek justice must be fully respected.

The Greek goverment, in its political position, had from the first voiced opposition to the attempted coup and indicated that those responsible were not welcome in Greece, Tsipras added.

Yildirim repeated Turkey's position for their extradition while acknowledging that it was an issue for justice to decide, "while the administration must do its own part."