The UN chief said there was "slow progress" on the core issue of the island's future security, an issue that could unlock an overall peace accord.
United Nations Secretary-General Antonio Guterres on Friday urged leaders of ethnically divided Cyprus to grasp a 'historic opportunity' for peace, but acknowledged a lot of work was required.
Guterres joined the Greek Cypriot and Turkish Cypriot leaders and representatives from Britain, Turkey and Greece at the Swiss Alpine resort where negotiations for a peace deal are taking place.
"The voices in support of a solution are indeed getting louder. At the same time there is no doubt that some sensitive and difficult issues remain to be resolved," Guterres told reporters in the Alpine resort of Crans-Montana.
Cyprus is one of the world's longest-running political crises and the talks in Switzerland have been billed as the best chance for a lasting solution.
"This offers a historic opportunity to reach a comprehensive settlement to the conflict that has divided Cyprus for too many decades," Guterres said.
In the session on security and guarantees, "there were some new positions showing increased flexibility in some aspects", he said, without elaboration.
"But it is slow progress and many outstanding issues are still to be resolved," he said.
Addressing the opposite sides earlier, Guterres said in remarks that "the emotional and rational" Mediterranean sides of Greeks and Turks are a strength that could be used to resolve problems holding back an agreement, according to an official who spoke on condition of anonymity because he's not authorised to disclose details of the meeting.
The talks, that began on Wednesday, have made no real progress on the core issue of the island's future security, an issue that could unlock an overall peace accord.
Guterres sounded out Greek Cypriot leader Nicos Anastasiades, Turkish Cypriot leader Mustafa Akinci and top diplomats from Cyprus' "guarantors" — Greece, Turkey and Britain — on ways to bridge gaps preventing progress.
Turkey has rejected Greek and Greek Cypriot calls to remove all troops from breakaway northern Cyprus after the island is reunified as a federation. It insists that any peace accord should grant Turkish citizens the right to relocate and transfer money, services and goods to the European Union member island.
Although Cyprus joined the EU in 2004, only the Greek Cypriot southern part that is the seat of the island's internationally recognised government enjoys full benefits.
Cyprus was split in a Turkish military intervention in 1974, triggered by a brief Greek-orchestrated coup aimed at annexing the island to Greece.
Turkey supports the breakaway Turkish Republic of Northern Cyprus (TRNC), which Turkish Cypriots established in 1983 after years of failed negotiations to restore peace.
Two issues are vexing: Turkish Cypriot demands for a rotating presidency, and Greek Cypriot demands that Turkey pulls all its 30,000 troops off the island.
The Greek Cypriots are also demanding that Turkey renounces its position as guarantor. As outlined by the 1960 Treaty of Guarantee, Turkey, Britain and Greece have the right to intervene militarily on the island to preserve peace.
Turkey's Foreign Minister Mevlut Cavusoglu on Thursday said Greece and Greek Cypriots should "wake up from their dream" that Turkey will withdraw all of its troops from Cyprus and give up military rights there as part of any agreement.