He underlined the need for real progress in reunification talks during a live television address ahead of crunch week-long talks with Turkish Cypriot leader Mustafa Akinci in Mont Pelerin near Geneva from Monday.
The summit will focus on the key issue of territorial adjustments.
“There is no way I will accept a multi-party conference if there is no progress on territory and convergences in the adjustments to be made. Agreement on criteria means the submission of maps,” Anastasiades said.
Such progress will allow for a multi-party conference on security involving Greece, Turkey and Britain as “guarantor powers” of Cyprus's sovereignty.
“I hope the negotiations… will make such progress it creates the potential to move on to substantive discussions on security and guarantees,” he said.
Because of the make-or-break nature of the territory issue, the leaders agreed to hold talks outside Cyprus. It will be the first time that maps are brought to the table since the negotiations began.
The two leaders will seek to agree on the internal boundary between two future constituent states, allowing for the return of some areas in Turkish-held northern Cyprus to the Greek Cypriots.
Without agreement on territory there can be no decision on how many refugees can return to their former homes or how the plans for restoration, exchange or compensation for property will work.
Territorial adjustments are essential for any peace deal for the EU member state.
Anastasiades said that “for the first time” discussions on what will happen on the first day of a solution are at an “advanced stage”.
This would include the fenced-off “ghost town” of Varosha returned to its lawful inhabitants and a “significant number” of Turkish troops leaving the island, Anastasiades said.
After 17 months of negotiations, strong disagreement remains on the thorny issues of territory, security and guarantees which have yet to be discussed in detail.
“These are crucial to the end result,” said Anastasiades.
He said the aim was still to achieve a Cyprus solution this year.
UN chief Ban Ki-moon will launch the talks in Switzerland. EU foreign affairs chief Federica Mogherini has said a Cyprus settlement would be a “game changer” for the region at large.
The long-stalled peace talks — in what is seen as the last best chance to reunify Cyprus after four decades of division — began in May 2015.
Any agreement reached will be put to simultaneous referendums on both sides. Previous talks have failed over property compensation, territorial adjustments and security in a post-settlement Cyprus.
Cyprus has been divided since 1974, when Turkish troops occupied its northern third in response to an Athens-inspired coup seeking union with Greece.