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Guterres invited Greek Cypriot leader Nicos Anastasiades and his Turkish Cypriot counterpart Mustafa Akinci for the meeting to salvage a two-year diplomatic effort aimed at achieving a historic settlement in Cyprus.
UN-led talks hit a wall in late May 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.
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."
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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."
Cyprus talks have hit an impasse over Greek Cypriot demands that the withdrawal of Turkish troops be discussed at a conference in Geneva as part of security arrangements.
The Turkish Cypriot side maintains 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 30,000 troops in the north of the island.
The government's drive to explore for offshore oil and gas has also clouded negotiations, with Ankara calling for it to be halted until a settlement has been reached.
"What we need from now on is political will and determination, more than ever," said Akinci.
Guterres smiled, stood between the two leaders and shook both their hands as the meeting got underway.
The leaders are expected to discuss the way forward over dinner and try to agree on next steps.