Espen Barth Eide said many issues dividing the two sides had been resolved as the talks on reunification of the Mediterranean island entered the third day.
The UN envoy for Cyprus said on Wednesday the ongoing talks in Geneva aimed at reuniting the divided island are "on track" as many issues between the two sides had been resolved.
Espen Barth Eide, however, said that there was "still work to do" in the negotiations between Greek and Turkish Cypriots.
Eide, a former Norwegian foreign minister, is overseeing talks between Turkish Cypriot leader Mustafa Akinci and Greek Cypriot leader Nicos Anastasiades.
"We have dealt with some of the most difficult issues. We have touched upon almost all of them, we have solved many of them and we are close to resolving some other issues," Eide said.
Talks between the two sides moved to Geneva on Monday after 18 months of intensive peace talks.
While Ankara has a military presence on the island state, both sides agree that a dialogue is the best possible solution.
TRT World 's Ediz Tiyansan reports from Geneva.