President Nicos Anastasiades and Turkish Cypriot leader Mustafa Akinci said they hoped for a peace deal in 2016.
The latest round of negotiations aiming at reunification of the divided island has been going on for more than seven months.
The Turkish-controlled north broke away in 1974 after a Greek-inspired coup.
Nicos Anastasiades said his wish was for Greek and Turkish Cypriots to be able to live peacefully together in a reunified Cyprus, while Mustafa Akinci said he hoped 2016 would bring lasting peace for all.
“I wish the New Year will bring lasting peace, serenity and prosperity to all Cypriots,” Mustafa Akinci was quoted as saying by the Cyprus Mail.
According to the Cyprus Mail, Nicos Anastasiades and Muastafa Akinci will meet three times in January.
In 2004, Greek Cypriots rejected a UN plan to reunify the island. They were unhappy at limits on their right to return to property in the Turkish north.
Turkish Cypriots voted in favor of the plan.
The self-declared Turkish Republic of Northern Cyprus is diplomatically isolated, recognized only by Turkey.
UN peacekeeping forces estimate that 165,000 Greek Cypriots fled or were expelled from the north, and 45,000 Turkish Cypriots from the south, although the parties to the conflict say the figures are higher.
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