If Turkey and the island's minority Turkish Cypriots want a solution, "there can neither be occupation troops nor guarantees", Greek President Prokopis Pavlopoulos said after talks in Nicosia with his Cyprus counterpart Nicos Anastasiades, the Greek Cypriot leader.
Anastasiades, whose country has been a European Union member since 2004, said: "Our common goal is to finally achieve a solution that is fully compatible with the European acquis (EU legislation)...
"Without the need to have any third country as a guarantor or troops of any country staying to protect supposedly one or the other community."
UN-backed negotiations in the Swiss resort town of Mont Pelerin include Greek Cypriot and Turkish Cypriot representatives as well as officials from Ankara, Athens and former colonial power Britain.
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Those parties were also in Geneva last week trying to reach a deal to reunite Cyprus, which has been divided since 1974 when Turkish troops invaded its northern third in response to an Athens-inspired coup seeking union with Greece.
Anastasiades and Turkish Cypriot leader Mustafa Akinci have been holding direct talks at various locations over the past 20 months on how to forge a unified, two-zone federation.
There is general consensus that the guarantor power system needs to change, although the fate of some 30,000 Turkish troops deployed in the north remains an obstacle, with Ankara insisting they will not be withdrawn.
In Mont Pelerin, technical experts are trying to craft ideas for a new security system that can be weighed by senior political leaders.
Greece, like Britain, has said it is happy to do away with the guarantor power arrangement but has insisted on the end to the Turkish military's "occupation" of northern Cyprus.
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