"Tomorrow is going to be an important day as you know Secretary-General is arriving for the second day and we hope that with his contribution we finally conclude an agreement that is why he is coming," Akinci told reporters after meeting in Crans-Montana with representatives from the Greek Cypriot sides, EU and three guarantor nations -- Turkey, Greece and the U.K.
"We very much hope that what he has already started will be developed tomorrow so that it will help us to reach an comprehensive settlement," Akinci said.
"We are hoping that tomorrow will be intense and productive day for all people in Cyprus," he said.
Akinci said the proposal from Greek Cypriot side would not bring a solution as there was nothing new in it.
"We need reciprocal steps and tomorrow is the time for that," Akinci said.
"Tomorrow must be a decisive day for Cyprus," Akinci said, adding the prime ministers of the guarantor countries would not join the talks.
Turkey's Prime Minister Binali Yildirim and his Greek counterpart, Alexis Tsipras, spoke via telephone late Wednesday about a permanent solution for the island.
The leaders agreed it was possible only with equal rights for both communities, according to sources from the Turkish prime ministry who spoke on condition of anonymity dues to restrictions on speaking to media.
On Tuesday, Cavusoglu criticized Greek Cypriots for not showing "good intentions and flexibility" in the talks taking place in the Swiss resort of Crans-Montana.
"If there is to be a solution, we should decide this week, because this is the last conference," Cavusoglu had said.
Guterres left the Swiss resort Saturday after participating in the Cyprus conference a day earlier, along with Turkish and Greek Cypriot leaders as well as the guarantor countries.
The latest round of Cyprus talks in Crans-Montana began June 28.
On Monday, the UN received proposals from the Turkish and Greek Cypriot sides, as well as from the three guarantor nations.
The UN is seeking a peace deal to unite Cyprus under a federal umbrella, which could also define the future of Europe's relations with Turkey, a key player in the conflict.
The Eastern Mediterranean island has been divided since 1974, when a Greek Cypriot coup was followed by violence against the island's Turks, and Ankara's intervention as a guarantor power.