Ban praised both men for achieving "significant progress" in the UN-backed peace process which began 18 months ago.
"At the same time a number of sensitive and difficult issues still remain," he told reporters before talks began.
"The two leaders have reached a critical juncture in their talks. I encourage them to make the most of the moment and the momentum," he added."The prospect of a solution in Cyprus is within their reach. Expectations in both communities are high," he added, without taking questions about how the U.N. might try to steer the two sides to an agreement.
Cyprus has been divided since 1974, when Turkey carried out a military intervention into its northern third as a guarantor power in response to an Athens-inspired coup seeking union with Greece. After the intervention, the Turkish Republic of Northern Cyprus (TRNC) was founded under the leadership of its late president Rauf Denktaş.
The last major peace push collapsed in 2004 when a proposal worked out by then-UN chief Kofi Annan was accepted by most Turkish Cypriots but resoundingly dismissed by Greek Cypriots in twin referendums.