At least 79 people have died and more than 100 have been rescued after their fishing boat sank off southern Greece, the BBC reports.
But survivors have suggested as many as 750 people may have been packed on to the boat, with reports of 100 children in the hold.
Greece says it is one of its biggest ever migrant tragedies, and has declared three days of mourning.
Authorities say their offers of aid were refused but they are facing claims of not doing enough to help.
The boat went down about 80 km south-west of Pylos after 02:04 on Wednesday morning local time, according to the Greek coastguard.
The EU’s border agency Frontex said it had spotted the boat early on Tuesday afternoon and immediately told Greek and Italian authorities. The coastguard said later that no-one on board was wearing life jackets.
In a timeline provided by the coastguard, it said that initial contact was made with the fishing boat at 14:00 (11:00 GMT) and no request for help had been made.
It said the Greek shipping ministry had made repeated contact with the boat and was told repeatedly it simply wanted to sail on to Italy. A Maltese-flagged ship provided food and water at around 18:00, and another boat provided water three hours after that, it added.
Then at around 01:40 on Wednesday someone on the boat is said to have notified the Greek coastguard that the vessel’s engine had malfunctioned.
Shortly afterwards, the boat capsized, taking only ten to fifteen minutes to sink completely. A search and rescue operation was triggered but complicated by strong winds.