The death toll rose Monday to 62 people, a coast guard official told AFP - and that number looked likely to increase.
Firefighters from the town of Cutro readied a speed boat Monday to head out on a fresh search of the area as helicopters flew overhead.
At Le Castella, where a 15th century fortress dominates the shoreline, an AFP journalist witnessed the coastguard recovering the body of a woman who looked to be in her early 20s.
Sergio di Dato, head of the Doctors Without Borders (MSF) team offering psychological support to the survivors, said there were cases of children orphaned in the disaster.
"One Afghan 12-year-old boy lost his entire family, all nine of them - four siblings, his parents and other very close relatives," he told journalists.
Save the Children charity said on Twitter it was supporting survivors from Afghanistan, Pakistan, Somalia and Syria, including 10 minors who had been travelling with their families.
"There are many missing minors," it wrote.
The charity said survivors described how "during the night, near the coast, they heard a loud boom, the boat broke and they all fell into the water."
The survivors were "in shock... some say they saw relatives fall into the water and disappear, or die".
David Morabito, a rescue diver in Calabria, told Rai state broadcaster he had recovered the bodies of young twins from the water.
"When you see the little, lifeless bodies of children, those images pierce your heart," Morabito said.
The boat was reported to have set sail from Izmir in Turkey last week. Three suspected human traffickers were arrested and police were searching for a fourth, media reports said Monday.
The disaster has further fueled the debate in Italy over search and rescue measures for saving migrants who run into trouble on the Central Mediterranean route, which is the world's deadliest.
Far-right Prime Minister Giorgia Meloni, elected in September, has pledged to curb migrant arrivals.
Her government pushed through a controversial law last week that forces migrant aid charities to perform only one life-saving rescue mission at a time before heading directly to ports, which are often far away.
Critics say the measure violates international law and will result in more people drowning.
According to the interior ministry, nearly 14,000 migrants have arrived in Italy by sea so far this year, up from 5,200 over the same period last year.