"Reaching a mutually acceptable conclusion will require courage, flexibility and vision as well as a spirit of compromise," Ban told reporters.
Cyprus was divided in a Turkish invasion in 1974 triggered by a short-lived Greek-inspired coup. Decades-old attempts to resolve the conflict have failed.
"I am under no illusion that the Cyprus problem is easy to solve or about the difficulties that you face. At the same time, I am confident that a solution is possible and within reach," Ban said.
Alexander Downer, a former Australian foreign minister assigned as UN special envoy for Cyprus, said on Friday that progress had been made on some aspects of discussions between the sides on how to co-govern the island in a future peace deal.
Any agreement between Christofias and Talat has to pass a referendum on both sides of the island.
Turkey's bid to join the European Union hinges partly on a Cyprus deal. Greek Cypriots represent the island in the bloc and will not agree to Ankara joining until the island's division is resolved.
Diplomats are concerned chances of a deal could recede if Talat, viewed as a moderate, loses a leadership election in northern Cyprus - a breakaway state recognised only by Ankara - in April. Veteran Turkish Cypriot politician Dervis Eroglu, a hardliner leading in opinion polls ahead of the 18 April vote, advocates a two-state deal, rejected outright by Greek Cypriots.
"I'm not optimistic. They left too much too late to intensify the talks, and that is not enough to get Talat re-elected," said a diplomat in Nicosia, Cyprus's ethnically-split capital.
Without a deal on Cyprus Turkey cannot join the European Union because Greek Cypriots, who are in the EU and view Ankara as the primary source of the conflict, will block it.
Growing frustration in Turkey at the slow pace of its EU talks may also take its toll, said Hubert Faustman, associate professor of history and politics at the University of Nicosia.
"The worse it looks in Turkey's EU relations the less inclined Ankara may be to play ball on Cyprus," Faustman said.
(EurActiv with Reuters.)
