After a dinghy carrying approximately 40 people sank late on Wednesday, the coast guard said that 15 remains had been found close to the Lesbos island in the east.
Three of the five passengers who were found on a rocky outcrop close to where the ship sank were among the five who were saved.
A second rescue operation was started hundreds of miles to the west, close to the island of Kythira when a sailboat carrying about 100 migrants capsized late on Wednesday after colliding with rocks.
After that boat ran aground near the east coast of the island's tiny port of Diakofti, authorities reported that 30 passengers had been saved.
Fire department personnel deployed ropes to assist migrants as they scaled seaside bluffs. Local authorities announced that a nearby school would be opened for the rescued to stay. Also anticipated to arrive on Thursday were navy divers.
The majority of migrants entering Greece come from the neighbouring country of Turkey. Still, smugglers have shifted their tactics recently to escape the heavily monitored waterways around the Greek islands that border Turkey.
Kythira is located around 400 km west of Turkey on a path smugglers frequently use to skip Greece and travel straight to Italy.