Greek officials said 19 people died and 138 were rescued near Kalymnos.
Three others died off Rhodes and three were missing. Six were rescued there.
Greece’s PM Alexis Tsipras said he felt “shame” over “the inability of Europe to deal effectively with this human drama”.
Speaking in parliament, the left-wing Syriza leader condemned the “level of debate at a senior level, where one is passing the buck to the other” in the EU.
“Crocodile tears are being shed for the dead children on the shores of the Aegean, because dead children always arouse sorrow, but what about the children that are alive who come in thousands and are packed on the refugee trail? Nobody cares for them,” Alexis Tsipras added.
Meanwhile, rescuers in southern Spain are searching for 35 refugees missing after their boat broke up on its way from Morocco. Four bodies have been found.
The unseaworthy, overcrowded boat set off from Alhucemas. Fifteen refugees were rescued.
In recent months the main migrant influx has been to the Greek holiday islands lying off Turkey’s Aegean coast.
In this week’s previous sinking in the Aegean, Greek authorities confirmed the deaths of 16 refugees off Lesbos after their boat broke up in rough seas late on October 28. Rescuers managed to save 274 people.
Thousands have been arriving on Lesbos every day after making the dangerous journey from Turkey. People traffickers usually pack them onto unseaworthy boats, often inflatable dinghies.
The UN estimates that more than 700,000 refugees have crossed to Europe by boat so far this year – many of them refugees from war-torn Syria. The approach of winter has so far done little to slow the flow.
The EU is deploying its Frontex border force to new “hotspots” – refugee reception centers in Greece and Italy where local officials are overwhelmed by the numbers. Frontex aims to help speed up the registration of refugees.
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