Two women, one of them pregnant, were recovered alive.
"According to the pregnant woman, there were 25 people on board the boat that sank," the coastguard spokeswoman said.
The dead apparently include nine men, four women and two children, she said.
Greek authorities had received no distress call prior to finding the bodies, the coastguard spokeswoman said.
Several vessels are continuing the search.
Weather conditions in the area are mild.
Greece's Aegean Sea islands are a primary transit point for refugees and migrants seeking to reach Europe from Turkey.
Over a million people have landed in Greece since 2015, most of them fleeing war in Syria.
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24 April 2017 - 13:41
News ID: 825704
(AhlulBayt News Agency) - Greece's coastguard said Monday at least 15 people including children have died in a suspected migrant boat sinking off the Aegean island of Lesbos.