Circumstances of the sinking of the vessel on Wednesday afternoon were unclear. Smugglers had to force passengers onto the boat at gunpoint because they were fearful about the seaworthiness of the vessel, Greek state television quoted witnesses as saying.
It sank when its upper deck crammed with people collapsed onto the lower desk, broadcaster ERT reported.
Elsewhere, another 123 people were rescued off the islands of Samos and in another incident off Lesbos. In total, 16 people drowned on Wednesday, including 11 children, the coast guard said. A baby has been missing for more than 12 hours.
Doctors and volunteers on Lesbos made desperate efforts to help a baby breathe, TV footage showed. Some of the survivors were sheltered in a chapel, a Reuters witness said.
The latest sinkings came just after EU leaders met on Sunday and agreed to boost cooperation and provide UN-aided housing for 100,000 people, half of them in Greece. The EU is expected to cover costs for accommodation for 20,000 in leased apartments in addition to temporary camps for 30,000 people.
But nations needed to stop fudging responsibility for the crisis, said German Foreign Minister Frank-Walter Steinmeier.
"I am convinced that we won't get anywhere if we just point the finger at each other, if one considers that the responsibility lies with the other," Steinmeier, who was in Athens, said during a meeting with Greek President Prokopis Pavlopoulos.
"It's clear that Greece - which is trying to get back on its feet right now - is feeling this influx as a particular burden," he told a Greek newspaper. "We will really support Greece in dealing with these big challenges."