In addition, Ankara has demanded from Brussels to open five new negotiating chapters and accelerate talks on Turkey’s accession to the bloc if an agreement on Cyprus reunification is sealed.
"We will not lift our veto on those chapters," Cyprus Foreign Minister Ioannis Kasoulides told Politico.
The diplomat underscored that his priority is the negotiations over the reunification of the Greek and Turkish halves of the island.
"When we resolve the problem, everything will be lifted," he added.
EU leaders are due to approve the agreement during a meeting on March 17-18 in Brussels.
In 2004, Cypriot Greeks rejected reunification at a referendum.
Nicosia fears that if it lifts its veto on admission talks with Turkey Greek Cypriots reject the decision.
"If the president says yes [to talks with Turkey], without advancements on the talks, the domestic front will be weakened and the chances for a referendum for a yes will be far less," the minister said. "Why don’t they leave us alone to negotiate and finish the issue of Cyprus first? And then everything will fall into place."