The latest UN-brokered negotiations between Anastasiades and his Turkish Cypriot counterpart Mustafa Akinci held in Switzerland this month ended yesterday with no agreement, with the two sides still far apart on the key issue of land-for-peace.
"I want to assure that I am determined and ready to take the necessary steps to continue the dialogue," Anastasiades said in a televised address today.
"I am ready to continue the dialogue where it broke off," adding that he was in touch with EU leaders to keep the "door open" for talks.
The much-heralded talks were supposed to produce a map of the internal boundaries of a future federation on the island to pave the way for a deal by early next year.
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But like the five days of discussions earlier this month, negotiations broke down, with each side blaming the other for the lack of progress.
Ban said he will be in contact soon with the leaders to discuss the next steps with just five weeks to go before the UN chief hands over to Antonio Guterres to lead the world body.
"Especially in a region and in a world marked by increasing tension, they must not let this historic opportunity slip," he added.
Cyprus is one of the world's longest-running geopolitical disputes and has been a key stumbling block in Turkey's EU accession bid.
Turkish Cypriots made up just 18 per cent of the island's population in 1974, but they currently control more than a third of its territory.
Anastasiades said the talks broke down on the issue of territorial adjustments because the "Turkish Cypriot side didn't show the required flexibility despite our efforts."
He said he "deeply regretted" the negative outcome in Switzerland but said he would not allow the opportunity to settle the four-decade-long crisis "to be lost".