The vessels had been trying to enter Greece illegally when they overturned before dawn off the coast of the island of Samos near the Turkish coast. It was not immediately clear what caused the overloaded craft to capsize. This was the third fatal migrant boat disaster this year.
The Greek coast guard said 36 people 32 men, three women and a child were rescued, and two of them a man and a child were airlifted to a hospital on the mainland.
Coast guard officials recovered the bodies of two women, a man and a boy from the sea, and later found a further 18 bodies including three children inside the yacht after it was towed to Samos.
Survivors told the coast guard between 60 and 65 people had been on the 10-meter yacht and the two-meter dinghy that had set off from Turkey.
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"We can't give a precise number of missing people with any certainty," Coast guard spokesman Nikos Lagadianos told The Associated Press earlier, before the overturned yacht was searched.
Despite the deep financial crisis that brought Greece to the brink of bankruptcy four years ago, the country remains a major entry point for people from poor or war-ravaged parts of Asia and Africa seeking a better life in the 28-nation European Union.
Fatal accidents are frequent as migrants risk the dangerous sea crossing from Turkey. Before today's incident, 21 people had drowned in similar incidents since the beginning of the year. At least 21 people died and six are still missing after a similar accident in December 2012.