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.
The negotiations on the long-running Cyprus conflict are the best chance, but maybe not the last one, for Turkish Cypriots and Greek Cypriots to get an agreement, the UN envoy to the island says.
Mediators hope to help the leaders of the ethnically divided island of Cyprus find a breakthrough in stalemated reunification talks.
No agreement could be reached on the summit, but the UN says the peace process has not fallen apart.
Turkish Cypriot and Greek Cypriot leaders meet for the first time since talks broke off two months ago over a controversial law passed by the Greek Cypriot assembly.
Turkish Cypriot President Mustafa Akinci has said a Greek Cypriot parliament decision to celebrate a 1950 referendum in which Greek Cypriots voted to unite Cyprus with Greece must be rescinded before talks can resume.
Turkish Foreign Minister Mevlut Cavusoglu says a Greek Cypriot decision to mark a divisive day in which they voted to unite Cyprus with Greece demonstrates that Turkish Cypriots are still at risk.
Turkish Cypriots fear the marking of "Enosis Day" celebrates the ethnic cleansing of Turks from Cyprus.
The Turkish president told reporters that "a guarantee without Turkey is not possible," as the Greek and Turkish Cypriot leaders attended a press conference following talks in Geneva.
Espen Barth Eide said many issues dividing the two sides had been resolved as the talks on reunification of the Mediterranean island entered the third day.
Although both sides hope the talks in Geneva will result in progress, they also acknowledge significant disagreements remain between them over key issues such as the presence of Turkish troops on the island.
Greek Cypriot leader Nicos Anastasiades says he will return to peace talks with Turkish Cypriot counterpart Mustafa Akinci after receiving UN assurances following a diplomatic spat.
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