"It's a unique opportunity, because after all of these decades of division it is possible, it is possible to solve, and I really hope that this is the spirit by which everybody goes into this meeting," Espen Barth Eide told reporters in Geneva.
His comments came as rival Cypriot leaders were headed to Switzerland for a make-or-break summit aiming to seal a long-elusive peace deal for their divided island.
President Nicos Anastasiades, the Greek Cypriot leader, and his Turkish Cypriot counterpart Mustafa Akinci are to resume the UN-led reunification talks on Wednesday in the Alpine ski resort of Crans-Montana.
They will be joined initially at least by the foreign ministers from the so-called guarantor powers of Cyprus - Greece, Turkey and Britain - along with EU foreign policy chief Federica Mogherini.
But a positive outcome is far from certain.
UN-backed peace talks held in Geneva in January failed to make any headway, and Eide himself warned that "it is not going to be easy and there is no guarantee of success".
"This is work in progress, and it is hard work. There will be long days and hard work ahead," he said.
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.
Turkey maintains around 35,000 troops in northern Cyprus. The Cyprus talks moved to Switzerland after negotiations on the island hit a dead end more than two years into the UN-brokered process.
Top of the agenda during this round of talks is a new security arrangement for a post-settlement federal Cyprus. This would involve the guarantor powers, which retain the right of military intervention.
Unlocking security would allow Anastasiades, who heads the island's internationally recognised government, and Akinci to make concessions on other core issues.
But Eide warned that the two sides remained "diametrically opposed" on the that point.
Anastasiades's government, backed by Athens, is pressing to abolish the intervention rights and for Turkish troops to withdraw from the island on a specific timeline.
On the other side, the Turkish Cypriots and Ankara will argue to retainsome form of intervention rights and a reduced number of troops remaining in the north.
But Eide hailed that sides were "basically done" on four other chapters being discussed, revolving around governance and power-sharing, property, economy and EU matters.
And he stressed that they had made "unprecedented progress" on the sticky issue of territory, when the two leaders in January exchanged largely overlapping maps of their vision for the former British colony.
"My preference is to talk about this as the best chance... It will be extremely sad if it is wasted," he said.