The Greek coast guard said 13 of those rescued near the islands of Agathonisi and Farmakoniki were picked up by Turkish authorities, and the other eight by the Greeks. The survivors told authorities a total of between 37 and 40 people had been on board, and the coast guard said it was still searching for about 15-18 people.
Survivors had earlier told authorities they believed between 33 and 37 people had been on board.
Tens of thousands of migrants have made their way from the Turkish coast to Greek islands so far this year, hoping to make their way to more prosperous European Union countries.
The numbers have overwhelmed Greek authorities, who have struggled to process and care for the large wave of migrants, most of whom are refugees from Syria and Afghanistan.
Earlier, the coast guard had said it had picked up 518 migrants from Monday morning to Tuesday morning in 14 incidents near the islands of Samothraki, Lesbos, Chios, Samos and Kos. Scores more arrive themselves on the shores of Greek islands in inflatable dinghies.