Many people are feared to have drowned after the boat they were being transferred to by traffickers capsized in the Mediterranean, survivors say.
The 41 survivors, refugees and other migrants mainly from East Africa, spoke to the BBC from the southern Greek city of Kalamata, where they are being held after their rescue.
They said up to 500 people had died, though there has been no official confirmation of the incident.
Earlier, six bodies were found after a separate incident off the Libyan coast.
Neither the Italian nor Greek coast guards have confirmed what would be one of the deadliest migrant boat disasters in recent years.
A Somali woman living in Egypt told the BBC Somali service that three of her relatives, whom she had not heard from since they set out for Europe on Thursday, had died.
The presidents of both Somalia and the self-declared Republic of Somaliland offered their condolences following the reports.
EU border agency Frontex has said that nearly 10,000 people tried to make the crossing to Italy last month, four times as many as tried in March 2015.
The deaths come on the eve of the first anniversary of the sinking of a migrant boat in the waters between Libya and Lampedusa in which up to 800 people may have drowned.
The UN says 180,000 people have attempted to reach Europe by sea this year, with nearly 800 lives lost.