But Greek officials and the International Organization for Migration (IOM) say that hundreds more migrants may have been on board.
The shipwreck is the deadliest off Greece this year.
The boat went down about 50 miles (80 km) south-west of Pylos after the coastguard said it had refused help.
The coastguard said the boat had been spotted in international waters late on Tuesday by an aircraft belonging to EU border agency Frontex. No-one on board was wearing life jackets, it added.
A few hours later, the boat capsized and sank, triggering a search and rescue operation, which was then complicated by strong winds.
Alarm Phone, an emergency helpline for migrants in trouble at sea, said the Greek coastguard was "aware of the ship being in distress for hours before any help was sent", adding that authorities "had been informed by different sources" that the boat was in trouble.
It added that people may have been scared to encounter Greek authorities because they were aware of the country's "horrible and systematic pushback practices".
The boat was reportedly on route to Italy from Libya, with most of those on board believed to be men in their 20s.
Survivors spoke of as many as 500 to 700 people on board and regional health director Yiannis Karvelis warned of an unprecedented tragedy: "The number of the people on board was much higher than the capacity that should be allowed for this boat."
Coastguard Cpt Nikolaos Alexiou told public TV that his colleagues had seen people packed on to the deck and that the boat had sunk in one of the deepest parts of the Mediterranean.
