UN envoy Eden Barth Eide held separate talks with rival Cypriot leaders Monday to try to revive peace negotiations after "very high hopes" of a breakthrough were dashed last week.

"What we are working on is to see how we can re-establish the momentum we had, but this has to be a decision made by the leaders," Eide told reporters after meeting President Nicos Anastasiades, the Greek Cypriot leader.

"And I am trying to facilitate that, but I cannot decide it over their heads," he said.

UN Secretary General Ban Ki-moon has warned Anastasiades and Turkish Cypriot leader Mustafa Akinci against missing a "historic opportunity" for peace.

The latest UN-brokered negotiations between Anastasiades and Akinci held in Switzerland earlier this month broke up with the two sides far apart on the key elements of a land-for-peace deal.

The talks in Mont Pelerin had been aimed at sealing a breakthrough to end decades of division on the Mediterranean island.

"Since there was some very high hopes and expectations for those specific meetings, it created a downturn in the mood surrounding the talks," said Eide.

"I don't principally see any unbridgeable issues but it is also very much about how to sequence things," he said, before crossing the UN-controlled buffer zone in Nicosia to also meet Akinci.

Cyprus has been divided since 1974 when Turkish troops invaded the northern third of the island in response to an Athens-inspired coup seeking union with Greece.

The much-heralded talks were supposed to produce a map of the internal boundaries of a future federation on the island to pave the way for a deal by early next year.

But negotiations broke down, with each side blaming the other for the lack of progress.

Cyprus is one of the world's longest-running geopolitical disputes and has been a key stumbling block in Turkey's EU accession bid.

Turkish Cypriots made up just 18 percent of the island's population in 1974, but they currently control more than a third of its territory.

It has always been agreed that some of the territory currently controlled by the Turkish Cypriots will be ceded to Greek Cypriot control in any peace deal.

The two leaders were close on the percentage of territory to remain under Turkish Cypriot administration in a future federation.

But they remain far apart on how many Greek Cypriots should be able to return to homes they fled in 1974, with Akinci determined to minimise the number of Turkish Cypriots who would be displaced for a second time.

Greek Cypriots want these issues resolved first, while the Turkish Cypriots want all outstanding disagreements to be tabled at a summit on security that would involve Britain, Greece and Turkey.

Anastasiades and Akinci have been among the most outspoken proponents of a deal within their own communities, but they would still have to sell any agreement they reach to their respective voters in separate referendums.