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The UN secretary-general says he is encouraged by efforts to find a permanent solution to the division of Cyprus.
But Ban Ki-moon said more courage was needed after talks with Turkish Cypriot leader Mehmet Ali Talat and Greek Cypriot President Demetris Christofias.
The two leaders have been locked in negotiations for the past 16 months.
Mr Ban said he was encouraged by a "shared commitment for a comprehensive solution as early as possible".
But while he spoke of convergence on some areas, it is clear that many issues remain unresolved, says the BBC's Tabitha Morgan in Nicosia.
'Grindingly slow' progress
Flanked by the two men after meeting each separately, and then together, Mr Ban said: "We will need even more courage and determination in the period ahead to bring these talks to a successful conclusion."
A UN-administered boundary currently separates Cyprus
Peace talks were launched amid much optimism and fanfare in September 2008. But progress has been grindingly slow and time may be running out to find a solution, analysts say.
The two leaders said there had been progress in the past three weeks over issues such as governance and power-sharing.
Whilst agreement appears near on certain issues, others such as territory and property, let alone security, seem seem harder to resolve, our correspondent says.
There are also concerns that talks could be shelved if Mr Talat, who is seen as a moderate, loses April's leadership election in northern Cyprus to nationalist candidate Dervis Eroglu, who is currently leading in opinion polls.
Northern Cyprus is recognised as a state only by Turkey.
Cyprus has been divided since 1974, when Turkish forces invaded the island in response to a Greek-led coup apparently aimed at making it part of Greece.
The last attempt at a negotiated solution to the Cypriot problem - in 2004 - collapsed when Turkish Cypriots voted in favour of a UN settlement plan, but Greek Cypriots rejected it.
As a result, Cyprus - or the southern part ruled by Greek Cypriots - joined the European Union that year, while the north remained effectively excluded.
File photo of Ban Ki-Moon. A UN buffer zone separates the two sections. 
A new set of talks are scheduled to attempt to reunite Cyprus, prompting UN Secretary General Ban Ki-Moon to say that a solution is "possible and within reach" when he arrived in the country yesterday for talks between Greek and Turkish-Cypriot leaders that will take place later today.

Progress have been slow for the peace talks, which started in September 2008,  but the UN chief said that a deal would require "courage, flexibility and vision as well as a spirit of compromise". "I am under no illusion that the Cyprus problem is easy to solve", he told reporters after he arrived in Larnaca yesterday in preparation for the talks with Greek Cypriot leader Demetris Christofias and Turkish Cypriot Mehmet Ali Talat today.

Ban said that "solving the Cyprus problem will give inspiration to all those around the world trying to solve other seemingly intractable problems and I'm looking forward to having good meetings with the leaders", with the Greek and Turkish Cypriot leaders saying that they are committed to finding a solution. Monday's talks will involve Ban holding talks with the two leaders individually, before chairing a meeting between the pair. Any deal that emerges will be a subject of two simultaneous referendums, one for each side of the border. Both sides agree that "nothing is agreed until everything is agreed".

Jonny Dymond, the BBC Europe correspondent, has expressed fears that time is running out on a solution. There are also worries that the fast approaching northern Cyprus leadership elections will mean that Talat is replaced by nationalist Dervis Eroglu, who is leading in opinion polls. If this were to happen, talks might be shelved.

Cyprus has been divided since 1974, after Turkish forces invaded after a coup led by Greece allegedly aimed to absorb it. Northern Cyprus is only recognised as a state by Turkey.