Greek Cypriot chief negotiator Andreas Mavroyiannis says an agreement on Famagusta between the two sides would "give great impetus" to the Cyprus peace drive.
Speaking in an extensive interview with Politis newspaper, Mavroyiannis said a settlement over Famagusta alone, could potentially create a domino effect with regards to resolving other disputes with the Turkish Cypriot side.
"For us, talks on Famagusta started a long time ago but what is different now is that we have the backing of both President Obama and the European Union," he said.
"We need to continue with this effort because the prospects [of reaching an agreement on Famagusta] are much better than before. It is not just a question of confidence-building measures but it will also give great impetus to the talks.
He added: "We believe that if the Famagusta talks reach a positive ending, then we would have resolved part of the territorial dispute and part of the property dispute."
The package being discussed over Famagusta involves Greek Cypriots giving their consent to the port of Famagusta being opened up under the supervision of the EU. In return, the rightful owners who originate from the town would be able to return.
Last week, Lisa Buttenheim, the resident United Nations envoy on the island, said President Anastasiades and Turkish Cypriot leader Dervis Eroglu would seek to forge a two-zone federation reuniting the island, which has been split since the Turkish invasion of 1974.
"The leaders expressed their determination to resume structured negotiations in a results-oriented manner," she said after reading out a joint-statement.
Both President Anastasiades and Eroglu will now leave key negotiators to thrash out the technical differences of the deal, the detail where talks typically flounder.
Not everybody is convinced. Coalition partner Diko and its recently appointed chairman Nicolas Papadopoulos says the text of the mandate is unbalanced in Turkey's favour and fired out a warning to President Anastasiades that his party could quit the government over the issue.
«The Turkish side achieves most of its long-standing ambitions, before talks have even started,» he argues.