Smugglers had charged the desperate men, women and children between $800 (£500) and $2,000 (£1,400) for the deadly voyage.
The 37 men, three women and a three-year-old child have been fingerprinted by Greek authorities and have been given papers allowing them to stay in the country for six months.
“The testimonies we gathered are heartbreaking,” said Daniel Esdras, the IOM’s mission chief in Athens.
“We await further investigations by authorities to better understand what actually happened and find hopefully evidence against criminal smugglers.”
The number of migrants known to have drowned in the Mediterranean so far this year is nearing 1,300, according to UNHCR figures, and campaigners fear the toll will rise as a crackdown on crossings between Greece and Turkey push refugees on to longer and more dangerous routes.
The Central Mediterranean route between North Africa and Italy has seen the bulk of disasters, with at least 380 people additionally drowning on the eastern route across the Aegean.
More than 180,000 refugees have arrived on European shores since January – a far greater number compared to the same period last year – but face ever tighter asylum restrictions and closed borders across the continent.
A spokesperson for the UNHCR called on nations to increase legal entry routes for asylum seekers, including resettlement programmes, family reunification, student and work visas and the possibility of private sponsorship.
“These will all serve to reduce the demand for people smuggling and dangerous irregular sea journeys,” he added.
Angela Merkel joined European Union officials on a trip to Turkey on Saturday in a bid to bolster the troubled refugee agreement, which has seen the country promised billions of Euros and visa concessions.
Human rights groups criticised a planned trip to what they call a “sanitised” refugee camp near the Syrian border, where Turkish guards have been accused of shooting asylum seekers fleeing worsening violence.