CRANS-MONTANA, Switzerland (Reuters) - Greek Cypriot and Turkish Cypriot leaders began talks on Wednesday aimed at reuniting the island after more than 40 years of division, in what some activists said could be the last chance of a settlement.

Greek Cypriot leader Nicos Anastasiades and Turkish Cypriot leader Mustafa Akinci met in the Swiss Alpine resort of Crans-Montana, joined by senior U.N. and European Union officials and the foreign ministers of Greece and Turkey.

U.N. mediator Espen Barth Eide said the best outcome in talks tentatively scheduled to last until July 7 would be a comprehensive agreement, which would be hard but not impossible to attain.

“If we take our time and we focus on the essentials, it’s not beyond reach, it could happen,” Eide told reporters.

The second-best outcome would be a breakthrough on key issues, confirming a shared intent to reunify the island but requiring more talks in Cyprus to wrap up a final agreement.

“If we don’t have either of those I don’t think we can talk of a success in Crans-Montana, so this is what we are working towards.”

Any deal would be put to a referendum in both Cypriot communities simultaneously some time later this year.

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Cyprus was split in a Turkish invasion in 1974, triggered by a brief Greek-inspired coup. Turkey supports a breakaway Turkish Cypriot state in northern Cyprus.

“GOING THE FINAL MILE”

“At the end of the day, of course, it is the responsibility of the conference participants to go that final mile, to think outside of the box, to try out some new ideas so we can go down from this beautiful Swiss mountain with a plan,” Eide said.

Jeffrey Feltman, U.N. Under-Secretary for Political Affairs, said he had been pleasantly surprised by the positive start to the talks, which began on the complex and divisive issue of security.

“What we heard this morning gave us the hope and the conviction that the leaders and the three guarantors have come to this conference with the determination to overcome challenges and resolve the issues,” Feltman said.

The talks involve three guarantor states, Greece, Turkey and Britain. British Foreign Secretary Boris Johnson and Europe Minister Alan Duncan left by helicopter before the talks had officially opened to head home for a parliamentary session.

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“UK support for a settlement of the Cyprus issue remains steadfast and the UK will continue to be represented during the Conference on Cyprus in Switzerland,” a British Foreign Office spokeswoman said.

Greek Foreign Minister Nikos Kotzias and Turkey’s Mevlut Cavusoglu stayed on.

The United Nations is seeking a peace deal which would unite Cyprus under a federal umbrella and which could also define the future of Europe’s relations with Turkey, a key player in the conflict.

Two issues are especially vexing: Turkish Cypriot demands for a rotating presidency, and Greek Cypriot demands that Turkey withdraws all of its 30,000 troops from the island and renounces its intervention rights.

In a statement, the group “Unite Cyprus Now” welcomed the summit “in what we fear could be the last chance to reunite our island”.

It called on Anastasiades and Akinci “who have made unprecedented progress in the negotiations to find a comprehensive solution to the Cyprus problem, to show the necessary leadership and courage to end the longstanding division”.