Guterres said UN-mediated talks in Switzerland offered a chance to reach a comprehensive settlement to the conflict that has divided Cyprus for "too many decades".
"I firmly believe that through determination and political will, it will be possible to clear this final hurdle to a comprehensive settlement," he told reporters.
Guterres arrived Friday at the talks in the Swiss Alpine resort of Crans-Montana to bolster efforts to reunify Cyprus and solve one of the world's longest-running political headaches.
Cyprus has been divided since 1974 when Turkish troops launched an invasion and later occupied its northern third in response to an Athens-inspired putsch seeking union with Greece.
More than 2,000 people are thought to have died during the offensive and the years of ethnic violence that preceded it.
Around 1,200 people are still missing, and more than four decades of mistrust between Greek- and Turkish-Cypriot communities have foiled successive reunification efforts.
Key to any deal would be the potential withdrawal of some of Turkey's 35,000 troops still stationed on the island.
In return, Turkish-Cypriots want guarantees against a repeat of the coup attempt as well as a rotating presidency to head up any future federal state.
President Nicos Anastasiades, the Greek Cypriot leader who heads the island's internationally recognised government, and his Turkish Cypriot counterpart Mustafa Akinci are representing their respective communities.
They are joined by delegations from Cyprus's so-called guarantor powers Greece, Turkey and Britain.
"Those gathered here today, the leaders, the communities in Cyprus, the guarantor powers, have a responsibility to grasp the opportunity for peace and to bring a comprehensive settlement owed to Cyprus," Guterres said.
"But there is still a lot of work to be done."
The Crans-Montana conference has been billed by the UN as Cyprus' best chance for peace and could last until July 7 if headway is made on a range of issues.
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