The agreement to resume negotiations on a historic deal was reached during a four-hour meeting between the two leaders and Guterres at UN headquarters.
Guterres had invited Greek Cypriot leader Nicos Anastasiades and his Turkish Cypriot counterpart Mustafa Akinci for talks to salvage a two-year diplomatic effort aimed at achieving a settlement in Cyprus.
Flanked by the two leaders, Guterres told reporters that all three had "agreed on the need to reconvene the conference on Cyprus in June."
The UN-led talks hit a wall nine days ago after the sides failed to agree on the terms to advance the reunification talks toward a final summit.
The eastern Mediterranean island has been divided since 1974, when Turkish troops invaded its northern third in response to an Athens-inspired coup seeking union with Greece.
The Greek Cypriot side demanded that the withdrawal of Turkish troops be discussed at a conference in Geneva as part of security arrangements.
The Turkish Cypriots maintained that the conference should focus on broader issues of power-sharing, property rights and territory for the creation of a new federation.
Following the meeting, Guterres said that "all agreed that the chapter on security and guarantees is of vital importance to the two communities."
"Progress in this chapter is an essential element in reaching an overall agreement and in building trust between the two communities in relation to their future security," he said.
The leaders agreed to continue negotiations on "all other outstanding issues, starting with territory, property and governance and power-sharing," said Guterres.
"All issues will be negotiated interdependently," said Guterres, stressing that "nothing is agreed till everything is agreed.
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