UN chief Ban Ki-moon expressed optimism that Greek Cypriot leader Dimitris Christofias and Turkish Cypriot President Derviş Eroğlu were on their way to resolving long-standing differences.
"Discussions have been positive, productive and vigorous," Ban told journalists, flanked by the two leaders at UN headquarters in New York.
"This has given me confidence that a comprehensive settlement can be achieved. Both leaders have assured me that they believe that they can finalize a deal," he said.
He said further efforts were needed over the next two months to move to the "end game" of negotiations.
Ban spoke after the United Nations hosted a meeting of Christofias and Eroğlu on Sunday and Monday at a secluded estate in Long Island, New York.
The United Nations has been trying for years to reunite Greek Cyprus, a Mediterranean island split between its Greek and Turkish Cypriot populations in 1974 after a brief Greek-inspired coup.
The conflict has bedeviled Turkey's attempts to join the EU, where an internationally recognized Greek Cypriot administration represents the whole island in the bloc.
The sides agree in principle to unite Greek Cyprus under a federal umbrella. But there are deep disputes on how to co-govern, territorial adjustments between two future constituent states, and the property claims of thousands of internally displaced people.
Christofias said that difficult negotiations lay ahead. "The target (until the summit) is to bridge the gap which divides the two sides on various core issues, which is difficult taking into account the differences. But it is not impossible," he said.
Eroğlu expressed optimism that talks were drawing to a conclusion. "Ban's statement that talks are coming to an end is especially pleasing," he told Turkish Cypriot television. "The Secretary-General made it very clear that first there will be the January summit, then a four or five-way conference after which it will be clear whether an agreement can be reached or not."
The summit, if successful, would pave the way for what Ban described as a "multi-lateral conference," a gathering which would include among others guarantor powers of Cypriot sovereignty which are now Turkey, Britain and Greece.
Sources say of particular difficulty were different interpretations of executive rule.
Greek Cypriots have proposed rotating presidency under a cross and weighted voting system. Turkish Cypriots, which initially backed such an option under a different leadership, now advocate rotating presidency with a separate ballot for each ethnic group.
Peace talks, which have been continuing since 2008, have shown advances on areas of the economy, EU issues and internal aspects of security.
But "there is still work to be done," said Ban, citing governance, property, territory and citizenship.
Cyprus is home to one of the world's oldest UN peacekeeping forces, which polices a buffer zone that splits the island.
The south is populated by Greek Cypriots, who represent the island internationally, and the north by Turkish Cypriots who run a state only recognized by Turkey.
The seeds of division were sown in the 1960s, when Turkish Cypriots left a power-sharing administration amid a constitutional crisis, just three years after independence from Britain.
The split has been thrown into sharper focus this year after Greek Cypriots launched exploratory drilling for natural gas off its southern shores, though the issue did not come up in peace talks, diplomats said.
Turkey warns the move will harm talks and says that any potential hydrocarbon wealth belongs to both communities on the island. Greek Cypriots counter it is their sovereign right to explore for hydrocarbons, and imminently plan a new licensing round to auction off exploration plots south of the island.