Muaz Mahmud’s wife and 2-month-old son barely had time to scream as the cold waters of the Mediterranean surged over their heads.

Minutes earlier, they had been forced by smugglers to abandon the boat they had chartered in Libya last week for a larger boat already packed with 300 migrants heading toward Italy.

As the bigger boat took on more passengers, it began to list, Mr. Mahmud said Thursday. When it capsized, hundreds of panicked people — many of whom could not swim — were thrown into the sea.

Mr. Mahmud and another survivor of last week’s shipwreck recounted grim details of the sinking, in which 500 passengers may have died, making it the deadliest episode for asylum seekers trying to reach Europe since more than 800 drownedlast April in a boat trying to reach Italy.