Eight migrants were missing near the Greek island of Lesbvs on Thursday after their boat collided with a Greek rescue vessel, the coastguard said.
Another 31 people of undisclosed nationality were rescued, it said.
A search by Greek and Portuguese patrol boats and an EU border agency helicopter was underway, it added.
The perilous Aegean Sea crossing from Turkey to Greece is claiming migrant lives almost each day.
On Wednesday, a woman, a young girl and a baby died after their boat sank off Lesvos.
The International Organization for Migration (IOM) says more than 590,000 migrants have reached Europes shores since January, while more than 3,000 have died or gone missing.
More than 450,000 of the total have arrived in Greece, most of them fleeing the civil war in Syria.
Athens and the UN refugee agency have both called on the European Union to open up more legal channels for people fleeing war and persecution, so that they do not have to risk their lives to reach safety.