Rival Cypriot leaders have agreed to resume UN-backed reunification talks in what was hailed Friday as a "significant development" after negotiations broke down in Switzerland last month.

The agreement was "an important development because it removes the problems created in Mont Pelerin without consolidating the deadlock with unforeseeable consequences", President Nicos Anastasiades said in a televised address.

"The momentum that existed has been preserved and can continue at the point where talks broke off" in the Swiss resort, the Greek Cypriot leader said.

Anastasiades said a prolonged deadlock could have killed off the peace process and that "political powers" had wanted the stalled negotiations to resume.

The decision to return to the negotiating table was taken during a UN-hosted dinner for the two leaders in Nicosia's UN-controlled buffer zone late on Thursday.

It was the first time that Anastasiades and his Turkish Cypriot counterpart Mustafa Akinci had met face-to-face since last month's disappointment in Switzerland.

There had been mounting international pressure for the leaders to pick up where they left off in an effort to reach a deal before the end of this year, although that deadline now appears to have lapsed.

"The leaders have decided to immediately re-engage in their negotiations and have instructed their negotiators to continue meeting in order to achieve further progress on all outstanding issues interdependently," a UN statement said.

"In line with their joint resolve to reach a comprehensive settlement as soon as possible, they further decided that they will meet in Geneva on 9, January, 2017," it added.

- Boundary proposals -

On January 11, they will present maps of their respective proposals for the internal boundaries of a future federation.

"From 12 January, a conference on Cyprus will be convened with the added participation of the guarantor powers (Greece, Turkey and Britain). Other relevant parties shall be invited as needed," the UN said.

Anastasiades said the Turkish Cypriot side had pledged to submit a map on territory in Geneva.

"Progress on the above issues will take us within reach of an agreement, creating the conditions and prospects for a successful outcome in the discussion of the fundamental issue of security and guarantees that will follow."

Crunch talks between the two leaders on ending the island's decades-old division collapsed with the two sides still far apart on the issue of territory and no date set for a new round.

Cyprus has been divided since 1974, when Turkish troops invaded the island in response to an Athens-inspired coup seeking union with Greece.

It has always been agreed that some of the territory currently controlled by the Turkish Cypriots will be ceded to Greek Cypriot control in any peace deal.

Turkish Cypriots made up just 18 percent of the island's population in 1974, but they currently control more than a third of its territory.

Just how much and which land they should give up has bedevilled four decades of peace talks.

There are also differences over post-solution security arrangements with Anastasiades wanting all Turkish troops on the island to leave but Akinci determined to keep a Turkish military presence.

- Guarantor powers -

UN envoy Espen Barth Eide was in Athens on Friday for talks with Greek leaders and was to travel to Ankara on Monday.

He said he "strongly supported the idea of a meeting at a highest level between Greece and Turkey" to discuss Cyprus.

"I'm trying to inspire that to happen because I think this is healthy, that those two (guarantor) powers have direct contact," Eide said.

"The purpose is not to solve all the questions but to have a better understanding of what we have to do and what to achieve in the conference."

Greece, like former colonial power Britain, has said it is willing to give up its right of intervention as a guarantor power. Turkey says it is ready to discuss security issues in five-way talks but without any preconditions.

Greece on Friday welcomed the resumption of talks.

"Athens is going to intensify its diplomatic efforts within the framework of the European Union so that there is a convergence of views on the crucial problem of security and guarantees," government spokesman Dimitris Tzanakopoulos said.

Anastasiades and Akinci have been among the most outspoken proponents of a deal within their own communities, but any agreement they reach will have to be approved by their respective voters.

In 2004, a UN-drafted peace blueprint was approved by Turkish Cypriots but resoundingly rejected by Greek Cypriots in simultaneous referendums.