By Michele Kambas and Tulay Karadeniz
GENEVA (Reuters) - The foreign ministers of Britain, Greece and Turkey met on Thursday to thrash out a security deal for a reunited Cyprus and end a conflict rooted in Britain's colonial past and Greek and Turkish rivalry in the region.
For the first time in decades, the three countries were to discuss a 1960 treaty cited by at least one of them in the past as a basis for intervening in the Mediterranean island.
Greek Cypriots and their ally Greece want an overhaul of the current security setup, while Turkish Cypriots and Turkey say it must be maintained.
"Continuing the security and guarantor arrangements, which have been the basis of security and stability on the island for the last 43 years, is a necessity given the situation in the region," Turkish Foreign Minister Mevlut Cavusoglu told a conference at the Geneva headquarters of the United Nations.
"We are expecting this issue to be evaluated with an understanding in line with the realities on the island."
Cyprus was split by a Turkish invasion in 1974 that followed a brief coup engineered by the military then ruling Greece. It has remained split ever since, with Turkish Cypriots in the north of the island and Greek Cypriots in the south.
The Geneva conference is being chaired by new U.N. Secretary-General Antonio Guterres, in his first major involvement in a conflict which has been on the world body's agenda for more than half a century.
European Commission President Jean-Claude Juncker was also in attendance. Cyprus is a member of the European Union, represented by the internationally recognised Greek Cypriot government. Recent hydrocarbon discoveries off Cyprus's shores could help the EU reduce its energy dependence on Russia.
BRITAIN BACKS A DEAL
Nicos Anastasiades and Mustafa Akinci, the respective leaders of the Greek and Turkish Cypriot communities, have been in Geneva for four days trying to reach a deal which would see the country reunited in a two-state federation.
British Foreign Secretary Boris Johnson said there was a "unique opportunity" to find a settlement.
"The fact that we have got this far is a real tribute to the courage and the determination of the leaders of the Greek Cypriot community and Turkish Cypriot community," he said in a post on social media.
"...The most important thing clearly is that both communities should feel secure about their futures and that is what the British government is here to help with."
Greek Prime Minister Alexis Tsipras could join the summit if there are prospects for a solution, his spokesman said in Athens.
Greek Cypriots want the guarantor system dismantled because of Turkey's invasion in 1974. Turkish Cypriots, who were targeted by Greek Cypriot nationalists before the war, want Turkish guarantees maintained.
Property rights are also an emotive issue for thousands of people uprooted in the conflict.
In a groundbreaking move on Wednesday, the sides submitted proposals on how to define the post-settlement boundaries between the two sides. The proposals ranged between 28.2 and 29.2 percent of Cypriot territory remaining under Turkish Cypriot control, down from about 36 percent now.
Some of the proposals are set out in maps presented by the two sides and then put into a U.N. vault. Little of their contents has been made public.
Media reports suggested that a Greek Cypriot map proposes the return of 91,000 Greek Cypriot refugees to an area which would be under Greek Cypriot control, while a Turkish Cypriot map would permit the return of about 65,000 to land returned.
There are some 165,000 Greek Cypriot refugees from 1974, who fled to the island's south, and about 40,000 Turkish Cypriots from the pre-1974 conflict and a U.N.-sanctioned population exchange in 1975.
Britain, the former colonial power in Cyprus, has offered to relinquish about half of the 98 square miles - equivalent to 3 percent of total Cypriot territory - London still administers as part of any final peace deal.
One of Britain's two bases in Cyprus, Akrotiri, is a Royal Air Force outpost which has been instrumental in attacking Islamic State targets in Iraq.
(Additional reporting by Tom Miles; Editing by Gareth Jones)