Updated

The rival leaders of ethnically divided Cyprus have agreed to immediately resume reunification talks, the United Nations said Friday, breaking a nearly two-week stalemate that threatened to sink 19 months of solid progress.

In a statement issued early Friday, the U.N. said Greek Cypriot President Nicos Anastasiades and breakaway Turkish Cypriot leader Mustafa Akinci agreed to meet in Geneva next month over four days to tackle the most difficult issues in the way of ending one of Europe's most intractable conflicts.

The talks starting Jan. 9 in the Swiss city will aim to hammer out an agreement on the pivotal aspect of how much territory each side will control in an envisioned federation.

They will also bring together Greece, Turkey and Cyprus' former colonial ruler Britain to decide on ensuring on-the-ground security after an accord is signed.

The U.N. said teams of negotiators from either side will step up meetings in Cyprus ahead of the Geneva summit to mark further progress on other issues that remain unresolved. The leaders will meet as necessary.

A 1974 Turkish invasion following a coup aimed at union with Greece split the island into an internationally recognized Greek-speaking south and a breakaway, Turkish-speaking north. A Turkish Cypriot declaration of independence is recognized only by Turkey which keeps more than 35,000 troops in the north.

The announcement came after Anastasiades and Akinci met over four hours at a dinner hosted by U.N. envoy Espen Barth Eide inside the U.N. controlled buffer zone that splits the capital Nicosia.

It was their first face-to-face meeting after talks in the Swiss resort of Mont Pelerin broke down last month amid disagreement over how many displaced Greek Cypriots would be eligible to reclaim lost homes and property in redrawn federal zones. Anastasiades wanted as many as 90,000 people to be able to reclaim homes and property, while Akinci offered a maximum 65,000.

Anastasiades said after the dinner that there's a good chance to wrap up most of the issues on which the two sides differ ahead of the Geneva meeting.

"I want to reiterate our determination and from what I've concluded the determination of the other side to finally create the kind of fertile ground that will lead us to a successful conclusion," Anastasiades said.