Two migrants drowned and about 30 were missing after their boats capsized off the eastern Greek island of Samos early on Monday in seas where hundreds have died attempting the crossing this year alone, the Greek coast guard said.
Thousands of migrants from Africa and the Middle East pack into often unsafe boats to get into the European Union via Greece, Italy, Malta and other coastal states.
The numbers have increased since "Arab Spring" uprisings triggered unrest across North Africa and civil war in Syria.
Two vessels carrying about 68 migrants capsized about four nautical miles off Samos in the eastern Aegean Sea, close to the Turkish coast, a coast guard official said.
"Two drowned bodies were found and 36 migrants have been rescued ... About 30 are missing," the official told Reuters.
Authorities said they did not yet know the nationality of the migrants. Two air force helicopters, assisted by two coast guard vessels, one navy warship and a cruise liner were searching for the missing, the coast guard official said.
Greece, Italy and Malta have repeatedly pressed European Union partners to do more to help them handle the large numbers of migrants.