The Greek coast guard said the boats sank before dawn on Monday off the Greek island of Samos, near the Turkish coast. Officials said at least 18 people drowned and 36 were rescued.
However more people remain missing. The nationality of the migrants, who had been attempting to enter Greece from Turkey, was not immediately clear.
Air force helicopters and several coast guard vessels are involved in the search and rescue mission.
Migrants from Africa, the Middle East and Asia often pack unsafe boats to get into Europe, with hundreds dying each year doing so. The numbers have increased since unrest began across North Africa and Syria.
Greece, Italy and Malta have repeatedly asked their fellow EU countries for help in handling the large numbers of migrants. Some 45,000 boat migrants, including thousands of children, made dangerous Mediterranean crossings to land in Italy and Malta in 2013, according to the International Organization for Migration (IOM).
More than 350 people died last October in a shipwreck off the Italian island of Lampedusa. The boat of mainly Eritrean migrants was trying to reach Europe.
jr/kms (Reuters, AP, dpa, AFP)