Turkish Cypriot and Greek Cypriot leaders on Wednesday, along with representatives of guarantor countries, started talks to solve the long-standing dispute on the divided Cyprus island.
The conference held by the UN began at Le Regent Congress Center in Crans-Montana, Switzerland.
Turkish Cypriot leader Mustafa Akinci and Greek Cypriot leader Nicos Anastasiades met during the conference, joined by the UN envoy Espen Barth Eide, Turkish Foreign Minister Mevlut Cavusoglu and Greek Foreign Minister Nikos Kotzias.
Eide is expected to hold a press conference at 2:30 p.m. local time (1630GMT) at Le Regent Congress Center.
The upcoming Cyprus peace talks in Switzerland are the "best, but not the last chance" to solve the long-standing dispute on the divided Mediterranean island, according to the UN chief's special adviser on Cyprus on Tuesday.
"It is a unique opportunity because after all of these decades of division it is possible to solve, and I really hope that this is the spirit by which everybody goes into this meeting," Eide told a news conference in Geneva ahead of Wednesday's talks.
Eide said that the UN would not submit a "common document" to guide the discussions on security and guarantees as it was announced earlier in June.
In a statement on Tuesday, UN Secretary-General Antonio Guterres said, "The opportunity for the reunification of Cyprus is now finally before us."
"I call on all concerned players to seize this opportunity, for Cyprus first and foremost, but also for the wider eastern Mediterranean region," he said.
Guterres urged all participants in the talks to "demonstrate the will and leadership required to conclude a comprehensive settlement".
On Monday, Turkish Cypriot President Akinci described the talks as a "decision conference" for the future of Cyprus.
"I will set out on this journey with this positive thought in mind and a cautious optimism," Akinci said.
The re-start of Cyprus conference for June 28 was announced earlier this month after Guterres met with Turkish Cypriot and Greek Cypriot leaders in New York.
The eastern Mediterranean island has been divided since 1974, when a Greek Cypriot coup was followed by violence against the island's Turks, and Ankara's intervention as a guarantor power.
Akinci and Anastasiades have been involved in reunification talks to create a federal state since May 2015.
The pair met several times in Geneva and Mont-Pelerin last year, but their last meeting in February was fraught with controversy over a Greek Cypriot decision to introduce a commemoration of the 1950 Enosis referendum on unification with Greece.
Both sides had agreed on most of the issues in the reunification deal but the sticking points, including a security and guarantee system, remain unresolved.