Speaking to reporters ahead of a summit in Brussels on Thursday, Anastasiades said: "If Turkey fulfills its obligations according to the Ankara Protocol and the negotiation framework, then there is no problem."
"But without it we could [do] nothing," he said.
Following a meeting with European Council President Donald Tusk on Tuesday, Anastasiades threatened to block any attempt to open new policy areas, or "chapters", on Turkey’s EU membership bid unless it follows the terms of a 2005 protocol.
This would see Ankara recognize Cyprus’s Greek administration and open Turkish ports and airports to Greek Cypriot cargo and passengers.
Cyprus was divided in 1974 after a military coup on the island led to Turkey’s intervention.
Recent negotiations, spurred by the election of Turkish Cypriot President Mustafa Akinci in April, are seeking to reunify the island under a federal system and the participants have spoken of their hopes of achieving agreement by the end of the year.
All 28 EU heads of government are gathering in Brussels on Thursday to discuss how refugees and migrants entering Europe via Greece could be sent back to Turkey.
Under Turkey’s proposal to the EU, the country wants the 28-nation bloc to "share the burden'' based on a formula of "for every Syrian readmitted by Turkey from the Greek islands, another Syrian will be resettled from Turkey to the EU member states".
Ankara also wants visa liberalization by June, speeding up Turkey’s accession talks, and additional three billion euros [$3.4 billion] to meet the needs of Syrian refugees in the country.
According to EU diplomatic sources speaking to Anadolu Agency on condition of anonymity, the two main issues at Thursday’s summit are making sure the return mechanism is in compliance with international and EU law, plus the Cyprus issue. An EU official said the purpose behind the deal is to stop the incentive of refugees seeking to enter Europe.
"If it doesn’t work and if it doesn’t [work] relatively quickly well then it was either a bad idea or it was badly executed because the very idea is that you can break the smugglers’ model and the incentives of getting on a boat and getting to the Greek islands as a means of getting to Europe," the official said.
Over the past year, hundreds of thousands of refugees have crossed the Aegean Sea to reach Greece. This has placed a huge strain on the austerity-hit EU member and threatened the EU’s internal open border system, as countries to the north of Greece impose frontier restrictions.