"We find ourselves before critical and defining developments for the future of our homeland," Anastasiades said in a televised Easter address.
The Mediterranean resort island has been divided since 1974 when Turkish troops invaded the northern third in response to an Athens-inspired coup.
Successive peace efforts between its Greek- and Turkish-speaking communities have stumbled over issues including territory and security.
The current process, which saw talks resume in May 2015, is seen by analysts as the best hope for a lasting peace deal.
Anastasiades and Turkish Cypriot leader Mustafa Akinci have agreed to schedule four new meetings, in a new phase of talks, with the first beginning on April 20.
"In order to achieve a solution acceptable by the people, we must establish conditions that will allow us to live in a well-organised European state without any dysfunctions or open wounds," the Greek Cypriot leader said.
Much of the progress in recent talks was based on the strong personal rapport between Anastasiades and Akinci, leader of the breakaway Turkish Republic of Northern Cyprus.
The Turkish-held north is recognised only by Turkey.
But a row over Greek Cypriot schools marking the anniversary of an unofficial 1950 referendum supporting Enosis -- union with Greece -- has eroded trust.
And the leaders are still far apart on core issues such as power sharing, territorial adjustments and property rights.
Also in the mix are Greek Cypriot presidential elections year and the search for oil and gas, which Ankara wants to see stopped until peace talks have reached an outcome.
Any peace accord must be put to a referendum for a final say.
