GENEVA (Reuters) - The leaders of both sides of ethnically divided Cyprus began new unification talks on Monday but sought to temper hopes of a swift breakthrough, though its U.N. envoy said a deal to resolve one of Europe’s most enduring conflicts was within reach.

Turkish Cypriot leader Mustafa Akinci and Greek Cypriot President Nicos Anastasiades, launched a week of consultations in Geneva to tackle dozens of disagreements stemming from the 1974 division of the Mediterranean island. The talks will focus initially on how to handle property disputes stretching back more than 40 years.

But with several past reconciliation efforts having failed, both leaders have been careful this week to cool expectations of a quick fix. The United Nations special envoy for Cyprus also said on Monday that the talks were open-ended.

“We are now in the final moment. We are now really in the moment of truth. This is actually where will find out if this can be solved,” said Espen Barth Eide, a Norwegian diplomat appointed to the U.N. envoy’s job in 2014.

“I’m not saying on a specific date. Because it’s open-ended,” told a news briefing, urging islanders estranged for decades to “seize the moment”.

The talks are scheduled to broaden on Thursday to include Britain, Greece and Turkey, the guarantor powers of Cyprus under a convoluted treaty foisted upon the former colony when it became independent from Britain in 1960.

Their concerns will include security, and specifically the role Turkey and its 30,000 troops stationed in northern Cyprus will play in any reunification of the country as a two-state federation.

The rival sides are poles apart on that issue.

Greek Prime Minister Alexis Tsipras and Turkish President Tayyip Erdogan discussed Cyprus by phone for more than an hour on Monday, a Greek government official said.

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“Concerning the process, the Greek Prime Minister expressed the view to the Turkish President that he will travel to Geneva only if it is apparent there is the possibility of a deal.

“The two agreed to reassess the situation on the eve of the conference,” the official said

EXPECTATIONS TEMPERED

Asked on arrival at the United Nations in Geneva if he was optimistic, Anastasiades said: “Ask me when we are finished.”

Akinci was equally circumspect, saying on Sunday: “We are not pessimistic, but I see no need for exaggerated expectations that everything will just happen. We are expecting a difficult week.”

New U.N. Secretary-General Antonio Guterres, who is expected to attend the conference on Thursday, has described the talks as an “historic opportunity” for a breakthrough.

But the issues are difficult. Power-sharing, redrawing territorial boundaries, and security issues in a future reunited homeland have all frustrated past negotiations.

Property rights are also a sensitive issue for thousands of internally displaced people who were driven from their homes in periods of conflict before, during and after Turkey invaded the island’s north after a brief Greek-inspired coup in 1974.

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A combination of restitution, compensation and exchange were being discussed on Monday, with International Monetary Fund and World Bank officials included in the talks, though it was unclear how any deal might be paid for.

MOMENTUM

Despite the expressed caution, mediators are keen to press on while both communities are led by political moderates.

Both Anastasiades and Akinci are from Limassol, a port city on Cyprus’s southern coast. Akinci belongs to a dying generation of Turkish Cypriots who speaks almost fluent Cypriot Greek.

Dozens of issues remaining after 18 months of talks in Cyprus need to be resolved in the next two days before the sides submit maps outlining their proposals for the future boundaries of the island’s two constituent states.

“It’s not easy to make these final agreements ... It is also possible because I don’t know any issue in these negotiations that really cannot be solved if sufficient will is available,” Eide said.

Any agreement must be put to separate referendums in the two communities, with diplomats anticipating a vote around June. A previous peace blueprint put to referendum in 2004 was accepted by Turkish Cypriots but rejected by Greek Cypriots.

Analysts see the talks as a unique opportunity to settle a conflict which has brought NATO members Greece and Turkey to the brink of war and which is an obstacle to Turkey’s ambitions of joining the European Union.

“If this time it fails between these two pro-solution leaders ... then a huge motivation will be lost,” said academic Ahmet Sozen, who has followed the on-off peace talks for years.

“The two leaders have reached a lot of convergences beyond any other set of negotiations in the past. That’s for sure. And it would be a sin to waste this.”