A previous conference in January involved the guarantor powers for Cyprus but they failed to agree on a post-peace security strategy.
"Currently, we have reached a critical juncture in the process, since discussions are underway for the next steps forward," President Nicos Anastasiades said Friday at a Council of Europe ministerial committee session in Nicosia.
"I have put forward a creative proposal as to the methodology we could adopt that would allow us to finally break the current impasse, bridge the differences, and establish the parameters," the Greek Cypriot leader said.
UN envoy Espen Barth Eide has been at the centre of shuttle diplomacy between Anastasiades and his Turkish Cypriot counterpart Mustafa Akinci on taking negotiations to the next level at Geneva.
Eide has said the rival leaders are ready for a final push but that "outstanding issues" had to be cleared up before a summit in Geneva.
"A number of substantial differences still remain… which are directly linked to our capacity as an EU member state, and the vital need for a reunited Cyprus to be a truly independent state," Anastasiades said on Friday.
The crux of the differences is what a new Geneva summit would try to achieve.
Anastasiades is believed to want to resolve how the map of a post-settlement Cyprus would look like and the issue of security arrangements to be tackled.
On the other side, Akinci wants a Geneva conference to focus on issues of power-sharing and political equality in a federal Cyprus following more than four decades of division.
A previous conference in Geneva in January involved the guarantor powers for Cyprus -- Greece, Turkey and Britain -– but they failed to agree on a post-peace security strategy.
The Turkish Cypriots want a summit in June as new oil and gas drills offshore Cyprus are expected in July -- a process which Ankara wants halted until the reunification talks have reached an outcome.
The two sides have been engaged in fragile peace talks since May 2015 that observers have seen as the best chance in years to reunify the island.
The talks have gone further than any previous peace initiatives over the decades.
Much of the progress until has been based on the strong personal rapport between Anastasiades and Akinci, leader of the breakaway Turkish Republic of Northern Cyprus.
The eastern Mediterranean island has been divided since 1974 when Turkish troops invaded the northern third in response to an Athens-inspired coup seeking union with Cyprus.
After a failed peace referendum on a UN blueprint in 2004, the Cyprus Republic now headed by Anastasiades joined the European Union as a divided country, while the Turkish-held north remains recognised only by Turkey.