"There have been difficult moments over the past months and there will likely be further difficulties and challenges ahead.
"At the same time, the Cyprus problem is not insurmountable and the negotiations which begin today can and must have a successful outcome," he said.
Barnaby Phillips, Al Jazeera's correspondent in Nicosia, the Cyprus capital, said there are still big potential problems that the two leaders need to settle, such as the restoration of property rights and the exact details of power-sharing.
He said: "More than 200,000 people mainly from the Greek side, lost their property during the fighting in 1974. Will they be allowed to go back to their homes? Will they be compensated?"
The Turkish minority is also concerned about whether foreign powers will still be allowed influence in the running of the island, he said.
"How will the two communities share power exactly in a way that enables the Turkish minority community to still feel secure? Will outside guarantors still be allowed some influence?"
"For the Greeks that's anathema... Whereas the Turkish minority feel some outside interference is vital for their security," Phillips said.
Wednesday's meeting, the fifth this year between the two leaders, will pave the way for substantive negotiations to begin on September 11, initially focusing on power-sharing.
Christofias and Talat are then expected to meet at least once a week.
The leaders have also agreed to set up a hotline so they can remain in constant telephone contact throughout the negotiations.
"We are confident that we will succeed in concluding an agreement and hopefully as soon as possible... and hopefully... this year," the Turkish Cypriot leader said.
"There is a common will and a common desire and a common effort to achieve this target," added Christofias.
The negotiation process has an open-ended timeline but the UN has warned that the talks cannot go on indefinitely without tangible progress.
The build-up to the talks had been clouded by the refusal of Turkish Cypriot authorities to allow Greek Cypriot pilgrims to travel via a town in the remote northwest of the island to attend a church service.
However, hundreds of Turkish and Greek Cypriot peace activists rallied on Monday night in the capital's buffer zone chanting for a reunified Cyprus.
Preparatory talks at committee level since March have been accompanied by confidence-building measures, notably the opening of a symbolic crossing in Ledra Street, which links the south and north of the island in the heart of old Nicosia.
It is the first intensive push for peace since a UN reunification plan was approved by Turkish Cypriots but overwhelmingly rejected by Greek Cypriots, just a week before the island joined the European Union in 2004.