The latest deaths came as Athens angrily defended its handling of the mounting refugee crisis in Europe and appealed for more help.
Four babies and 11 young children - six boys and five girls - were among those on the stricken wooden boat when it sank off the island of Farmakonisi, Athens News Agency reported.
Eight of the victims were found by coastguard frogmen in the hold of the boat.
The exact number of those aboard remains unknown but the ANA said it was overcrowded and went down because of high winds in the area.
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The coastguard was also still searching for four children missing after another boat capsized yesterday off Samos, a Greek island just off the Turkish coast.
The latest tragedies follow the death of a Syrian toddler whose lifeless body was photographed washed up on a Turkish beach last week, becoming a heartwrenching symbol of the plight of refugees fleeing war.
Interim Prime Minister Vassiliki Thanou today branded criticism of Greece, which has been on the frontline of the surge of migrants trying to reach Europe, as "unacceptable".
"Greece is strictly applying European and international treaties without ignoring the humanity of the situation," she said on a visit to Lesbos, an island which has been struggling with the massive influx.
German Chancellor Angela Merkel yesterday called on Athens, already grappling with a deep economic crisis, to make more effort to protect the EU's external borders.
"Greece needs to take its responsibility... We will also speak with Turkey.