The island has been divided into Greek and Turkish sides since a Greek Cypriot coup was followed by a Turkish peace mission to aid Turkish Cypriots in the north in 1974.
Greek Cyprus will approve Turkish Cyprus's direct trade with the EU if Turkey hands down the closed city of Maras in Northern Cyprus, also known as Varosha in Greek, to the UN, Mavroyiannis added.
Representatives from both Turkish and Greek Cyprus will visit Athens and Ankara in the upcoming weeks, the first time in nearly half a century.
"We would like to end this dispute. We are determined to make this vicious circle turn into a positive situation," Mavroyiannis told AA. "The solution of the Cyprus dispute will prove that there are more factors that unite us than the ones which divide us."
He reminded that Greek Cyprus approved the start of Turkey's EU accession talks in 2005 and said they believed Turkey's EU membership process would contribute to the solution of the dispute between the two sides on the island.
"The Cyprus dispute is not the only obstacle before Turkey's EU accession, there are other obstacles, but if this dispute is solved, the process for Turkey's accession to the EU will gain momentum," he said.