Although both sides hope the talks in Geneva will result in progress, they also acknowledge significant disagreements remain between them over key issues such as the presence of Turkish troops on the island.
The leaders of the Turkish Republic of Northern Cyprus and the Greek Cypriot Republic of Cyprus met on Monday to begin a week of talks with the aim of sketching out a deal to end decades of division on the Mediterranean island.
Hoping to succeed where others failed, Turkish Cypriot leader Mustafa Akinci and Greek Cypriot leader Nicos Anastasiades are in Geneva for three full days of discussions.
Other nations with an interest in the future of the island will join the talks on Thursday.
TRT World's Vanessa Conneely has more.
Asked how he felt about the talks, Anastasiades said: "Ask me when we are finished."
Disagreements over how Turkish and Greek Cypriots would share power in a unified state, property boundaries, and security issues have led to negotiations breaking drown in the past.
However, mediators are keen to make progress before domestic election cycles upset the process.
Leaving for Geneva on Sunday, Akinci described the talks as a "crossroads."
"We are not at a point where Geneva will mark the final conclusion. We need to be cautious," he said.
"We are expecting a tough week."
TRT World asked Dr Hubert Faustmann of the University of Nicosia about some of the challenges facing the talks.
A difficult past
The current division of the island came about in 1974, when Turkey entered the north in response to a short-lived Greek-backed coup aimed at unifying Cyprus with Greece as well as longstanding communal violence and the marginalisation of the Turkish Cypriot community.
Turkey says its intervention was justified on the basis of the 1960 Treaty of Guarantee, which gives Turkey, Britain, and Greece the right to take action to maintain Cyprus's independence and uphold the republic's constitution.
Today, the island of just over one million inhabitants is split between the Greek Cypriots in the south and Turkish Cypriots in the north, separated by one of the world's oldest UN peacekeeping forces.
The status of some 30,000 Turkish troops stationed in Cyprus's north is crucial. The Greek side insists they must all be pulled out, while the Turkish side says some must remain.
That issue will dominate discussions between Britain, Turkey, and Greece on Thursday.
Britain retains two strategically important bases on the island which currently are used in operations against Daesh.
London has said it would be willing to relinquish about 49 percent of the 98 square miles (254 square kilometres) it controls at the moment to make it easier to adjust current territorial boundaries.
Any agreement must be put to separate referendums in the two communities, with diplomats anticipating a vote around June this year if the peace talks succeed. A previous peace blueprint put to referendum in 2004 was accepted by Turkish Cypriots but rejected by Greek Cypriots.