A "clear understanding" has been reached at talks between Greek Cypriot and Turkish Cypriot leaders and their backers on what is needed to reach a comprehensive agreement to reunite the island, UN Secretary-General Antonio Guterres said on Saturday.

Guterres, who arrived on Friday on the third day of negotiations in the Swiss resort of Crans-Montana, has lent his weight to the effort to unite Cyprus under a federal umbrella.

He gave no details, but said in a statement that he had held a "positive, results-oriented" meeting with Greek Cypriot leader Nicos Anastasiades and Turkish Cypriot leader Mustafa Akıncı, as well as Greek Foreign Minister Nikos Kotzias and Turkish Foreign Minister Mevlut Cavusoglu that evening.

"A clear understanding emerged of the essential elements of a package that might lead to a comprehensive settlement in Cyprus," Guterres' spokesman said in a statement issued on Saturday as political-level talks continued after Guterres left.

"The Secretary-General remains fully engaged in these efforts to deliver a comprehensive settlement to the people of Cyprus."

Alan Duncan, Britain's minister for Europe, and Frans Timmermans, vice president of the European Commission, also participated, a UN spokesman said. Greece, Turkey and Britain are the three guarantor powers.

Cyprus was split in a Turkish invasion in 1974, triggered by a brief Greek-inspired coup. Turkey supports a breakaway Turkish Cypriot state in northern Cyprus.

Two issues have proved especially vexing: Turkish Cypriot demands for a rotating presidency, and Greek Cypriot demands that Turkey withdraws all of its 30,000 troops from the island and renounces its intervention rights.