Greek and Turkish Cypriot leaders are close to reaching a deal on unifying the island, according to the United Nations chief, who cautioned, however against any "quick fix" to end decades of division.

Speaking from Geneva, Switzerland, where talks aimed at ending 40 years of stalemate are currently under way, Antonio Guterres said that major work remained on how to implement and guarantee a final pact.

"We are coming very close to what is the settlement," Antonio Guterres told reporters in Geneva on Thursday, adding however that key issues remained unresolved.

"You cannot expect miracles of immediate solutions, we are not looking for a quick fix," he said. "We are looking for a solid sustainable solution."

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Thursday's multi-party talks follow three days of negotiations between Greek Cypriot President Nicos Anastasiades and Turkish Cypriot leader Mustafa Akinci aiming to forge a united, two-zone federation in the eastern Mediterranean island .

AL JAZEERA'S JONAH HULL IN GENEVA: The conference on Cyprus involving the Cypriot leaders and the foreign ministers of Greece and Turkey was only due to take place for the day on Thursday. Quite what happens next is unclear. Do the foreign ministers stay here and keep working into Friday and perhaps the weekend? What is clear is that deep differences have emerged - in part to do with the boundaries of a possible future federal state of Cyprus drawn onto maps and presented by the parties on Wednesday, but even deeper differences over the question of security. The Greek Cypriots want Turkey to remove an enormous contingence of soldiers that has been in the north of the island since 1974. Indeed, the Greek Cypriots would quite like to see the whole system of guarantorship relinquished - but what system will replace it? What guarantees will be acceptable to both sides no one knows, and given that these talks proceed on the basis that nothing is agreed until everything is agreed, it does seem clear that a deal isn't as close as many had hoped.

Diplomats believe moderates Anastasiades and Akinci represent the best chance in years to reunite the country. But there are obstacles ranging from property grievances of thousands uprooted in conflict, to more practical difficulties associated with power-sharing, and security.

The conference also included top diplomats from Greece, Turkey and former colonial ruler Britain - the island's guarantor powers which, under a 1959 agreement, have the right to intervene to protect of Cyprus's sovereign integrity.

Ankara used that pact to justify its 1974 invasion that divided the island, which came in response to an Athens-inspired coup seeking union with Greece.

The goal of the talks, Guterres said, was to find a new system that "guarantees the security concerns" of both the Greek Cypriot and Turkish Cypriot communities.

"We are at a starting point" on the question of security, he said.

"My hope is there will be a breakthrough", he continued, adding that Cyprus can be "a symbol of hope."

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The presence of about 30,000 Turkish troops in northern Cyprus is strongly contested by Greek Cyprians, which hinders the closing of a deal without their potential withdrawal.

Britain and Greece have said they are willing to do away with the guarantor power arrangement, but Turkey on Thursday made clear that it expects some form of the deal to be preserved.

"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 said on Thursday.

WATCH: Cyprus reunification - Hopes of a solution amid talks

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.

There are about 800,000 Greek Cypriots and 220,000 Turkish Cypriots.

Greek Cypriots hope to reach an arrangement that would see the return of their internally displaced people to their homes under Greek Cypriot control.

The 1974 invasion uprooted 165,000 Greek Cypriots, while about 40,000 Turkish Cypriots were displaced in intercommunal violence in the 1960s and a population transfer in 1975.