UN Secretary-General Antonio Guterres announced the new round of talks following a four-hour dinner meeting with the two leaders at UN headquarters in New York.
Guterres had invited Greek Cypriot leader Nicos Anastasiades and his Turkish Cypriot counterpart Mustafa Akinci to salvage a two-year diplomatic effort aimed at achieving a settlement in Cyprus.
Flanked by the two leaders, Guterres told reporters after the lengthy meeting that all three had "agreed on the need to reconvene the conference on Cyprus in June."
No firm date was announced, but Guterres said he would consult with Britain, the European Union, Greece and Turkey on the timing.
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 the conference in Geneva as part of security arrangements.
But 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.
Turkey maintains some 35,000 troops in the north of the island.
Talks on security
In January, an international conference on Cyprus had opened in Geneva with representatives from Britain, Greece and Turkey –- the island's three guarantor powers.
The talks had been widely seen as the best hope yet to reunite Cyprus.
But on May 26, UN envoy Espen Barth Eide was forced to admit that lingering differences were blocking the convening of a second conference on finalizing a deal.
At the opening of the meeting, Guterres posed for photographers, standing between the two leaders and holding each one by a hand to stress the need to work together.
In his remarks, Guterres said "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 added.
The UN envoy will work with all sides to prepare "a common document to guide the discussions on security and guarantees," said Guterres.
The leaders also agreed to continue negotiations on "all other outstanding issues, starting with territory, property and governance, and power-sharing," he said.
"All issues will be negotiated interdependently," added the UN chief, stressing that "nothing is agreed till everything is agreed."
Arriving at UN headquarters, Akinci told reporters that "the reason why we are here is the impasse created by one side's insistence on putting forward pre-conditions."
Anastasiades hit back, saying "I am not here for a blame game" and voicing hope that the meeting could "pave the way for a constructive dialogue, in order to reach, not just progress, but a settlement."
"What we need from now on is political will and determination, more than ever," said Akinci.
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