The first tragedy occurred off the island of Samos when a boat overturned just 20 metres from shore.
Ten bodies -- including six children, four of them babies -- were found in the vessel's cabin while that of a girl was washed up on the island, where dozens of refugees have perished trying to reach Europe in recent days.
Two others were still missing with coastguards saying 15 were plucked from the water.
Frontex also rescued three others, who said their boat was carrying 15 people when it sank in Turkish waters.
Also Read
Greek authorities and the Turkish coastguard "continue to search the zone to find the migrants who disappeared in the sinking, which probably took place off the Turkish coast," a representative of the Greek coastguard's press office told AFP.
The new sinkings add to a string of migrant boat tragedies since Monday off the Greek islands of Lesbos, Kalymnos and Rhodes in which more than 60 people have drowned, at least 28 of them children.
That followed another black day on Wednesday when 24 migrants -- 11 of them children -- died in five shipwrecks off Lesbos, Samos and Agathonisi.
With the arrival of rough winter weather, and fears that Europe is about to close its doors to refugees, more than 80 people -- most of them children -- have drowned trying to reach Greece in October, according to an AFP count.
Since the beginning of the year, 580,125 migrants have landed on Greece's shores, according to the UN refugee agency UNHCR, with a total of 723,221 crossing the Mediterranean to Europe.
He is to travel to Lesbos this week with the president of the European parliament, Martin Schultz, his office said.