UN Secretary-General Antonio Guterres and Cypriot leaders on Monday agreed to reconvene a peace conference this month on the divided island, his office said.
Turkish Cypriot President Mustafa Akinci and Greek Cypriot leader Nicos Anastasiades met Guterres in New York in search of a way forward in the talks.
"The Special Adviser of the Secretary-General, Mr. Espen [Barth] Eide, will engage with all participants in the preparation of a common document to guide the discussions on security and guarantees, based on the outcome of the meetings of the conference on Cyprus in Geneva and Mont Pelerin," a statement said.
The next step for the UN ahead of the peace conference would be to "reach out to the other participants of the conference: Greece, Turkey and the United Kingdom and the European Union as an observer", the statement added.
Prior to the meeting, Akinci told reporters the purpose of the meeting Sunday was to "discuss the bottleneck created by the other side's persistent preconditions".
The Eastern Mediterranean island has been divided since 1974, when a Greek coup was followed by violence against the island’s Turks, and Ankara's intervention as a guarantor power.
Akinci and Anastasiades have been involved in reunification talks to create a federal state since May 2015.
The pair met several times in Geneva last year, but their last meeting in February was fraught with controversy over a Greek Cypriot decision to introduce a commemoration of the 1950 Enosis referendum on unification with Greece.
Both sides had agreed on most of the issues in the reunification deal but the sticking points, including a security and guarantees system, remain unresolved.