"We are doing our best to resolve the Cyprus issue in the shortest possible time," he added.
UN Special Adviser Espen Barth Eide said that both leaders also discussed several other issues, including about governance, power sharing, property, territory and the EU.
Akinci said that European Commission President Jean-Claude Juncker was expected to visit the island and there might be a possibility of a trilateral meeting in the near future.
Akinci and Anastasiades are expected to gather again on July 27.
Peace talks were unilaterally suspended by the Greek Cypriot administration last October after Turkey issued an advisory on behalf of the Turkish Republic of Northern Cyprus for seismic research off the coast of Cyprus.
The island was divided into a Turkish Cypriot government in the northern one third and a Greek Cypriotadministration in the southern two-thirds after a 1974 military coup by Greece was followed by the intervention of Turkey as a guarantor state in Cyprus.
Border gates between the Turkish Republic of Northern Cyprus and Greek-administered southern Cyprus were opened on April 2003.
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