NICOSIA, Cyprus - The rival leaders of ethnically divided Cyprus have agreed to 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 UN 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 UN 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 UN envoy Espen Barth Eide inside the UN 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.

The decision to resume talks came amid much finger-pointing about who was to blame for the Mont Pelerin impasse.

According to a schedule for the talks, the two leaders will present respective maps on how much territory their federal zones should comprise on Jan. 11. An enlarged meeting on security that will include Greece, Turkey and Britain will take place the following day.

The Greek Cypriot side says federal boundaries should be redrawn in a way that would allow the majority of Greek Cypriots displaced by the invasion to reclaim homes and property. That would reduce the cost of a peace accord by limiting the amount of compensation that would be paid out to those who wouldn't be able to get property back and would help shore up support for a deal among the Greek Cypriot electorate when the deal is put to a vote in referendums on both sides.

Turkish Cypriots insist that territorial adjustments should keep the number of Turkish Cypriots who would be forced to relocate to the bare minimum.

Another key sticking point in talks is a Turkish Cypriot demand to cede Turkey the right to militarily intervene and to keep troops on the island under any deal. The minority Turkish Cypriots see Turkey's as vital for their security, while Greek Cypriots consider them as a threat undermining the island's sovereignty.

Military intervention rights were granted to Greece, Turkey and Britain under the island's 1960 constitution. The Greek government opposes keeping these rights in place after a peace deal.

The decision to resume talks comes after remarks by Turkey's President Recep Tayyip Erdogan earlier this week in which he suggested that Greek Cypriots won't be permitted to fulfil their goal of controlling the entire island. Anastasiades decried the remarks as unacceptable.