"Nicosia has been always ready for a dialogue but for that ... to be effective, it needs to be clearly defined based on international law, without blackmails or threats," Anastasiades said after talks with European Council President Charles Michel in the capital of Cyprus on Wednesday.
Turkey, Greece and Cyprus have been locked in a dispute over drilling rights in the region.
On Tuesday, Ankara said it had extended the operations of Yavuz, an energy drilling ship, in disputed waters off Cyprus until October 12.
An emergency meeting of EU leaders is scheduled for September 24-25, where the main issue will be the Turkey-Cyprus standoff with sanctions a possibility.
"In view of the EU Council meeting next week, we underscored the importance of staying united on the messages (to Turkey) and determined to implement our decisions if the illicit actions continue," Anastasiades said.
EU vows to defend Cyprus rights
Michel vowed that the EU will defend the rights of member state Cyprus in its dispute with Turkey.
"The European Union stands in solidarity with Cyprus as it faces a grave situation. That is why we have decided to call a summit on relations with Turkey," Michel told reporters after meeting Anastasiades, adding "I believe we must be very firm when it comes to defending the rights of all member states, including Cyprus."
Also on Wednesday, European Commission President Ursula von der Leyen told the European Parliament nothing could justify what she called Turkey’s intimidation of Greece and Cyprus in the eastern Mediterranean.
Greece and Turkey almost went to war in 1974 over Cyprus, which has since been divided, with the northern third run by a Turkish Cypriot administration recognized only by Turkey and the southern two-thirds governed by the internationally-recognized Greek Cypriot government.