Diplomats said it appeared unlikely there would be another vote to try to renew the mandate before it expires on April 30
Greece is one of the main routes into the European Union for asylum-seekers crossing from Turkey in flimsy, overcrowded rubber boats but the number of people arriving has fallen sharply in recent years and deadly shipwrecks in its waters have become rare.
Authorities said 21 people were rescued and three more were believed to be missing. Ten vessels and two helicopters were assisting in the rescue operation.
Nearly 1 million people, mainly Syrian refugees, arrived in the EU in 2015 after crossing to Greek islands close to Turkey.
About 6,500 asylum-seekers have arrived in Greece this year, most through its northerneastern land border with Turkey, according to data by the United Nations refugee agency UNHCR.