The pair met in Thessaloniki on Friday as part of the 31st Meeting of the Council of Ministers of Foreign Affairs of the Organization of the Black Sea Economic Cooperation (BSEC).
Venizelos called for the withdrawal of the Turkish research ship Barbaros off of the Greek part of the island and claimed its presence constituted a violation of Greek Cypriots' sovereign rights.
"Continuing negotiations, reaching a sustainable solution and eliminating unnecessary debates are what really matter in Cyprus," said Cavusoglu for his part.
The two ministers also took up regional issues.
The BSEC is a multilateral political and economic initiative aimed at peace, stability and prosperity in the Black Sea region.
Member states include Albania, Armenia, Azerbaijan, Bulgaria, Georgia, Greece, Moldova, Romania, Russia, Serbia, Turkey and Ukraine.