At least 62 migrants are confirmed to have died, with 12 children said to be among the victims, including a baby.
The vessel, thought to have carried some 200 people, broke apart while trying to land near Crotone on Sunday.
People from Afghanistan, Pakistan, Somalia, Syria, Iraq and Iran were said to be on board.
Bodies were recovered from the beach at a nearby seaside resort in the Calabria region.
The coastguard said 80 people had been found alive, "including some who managed to reach the shore after the sinking", meaning many more remain unaccounted for.
One survivor was arrested on migrant trafficking charges, customs police said.
Many of those on board were thought to be from Pakistan. Its Prime Minister Shehbaz Sharif on Monday said more than two dozen Pakistanis were believed to have been among the dead.
As assistance and relocation operations continue, a group of survivors of the deadly shipwreck are struggling to come to terms with the loss of their loved ones.
At a temporary reception centre in the town of Isola di Capo Rizzuto, some of them were crying without speaking, some were just staring into the void, wrapped in blankets.
"They are heavily traumatised," said Sergio Di Dato, from charity Médecins Sans Frontières (MSF). "Some children have lost their whole family. We are offering them all the support we can."
A 16-year-old boy from Afghanistan lost his 28-year-old sister, who died on the beach next to him. He can't find the strength to tell his parents.
A 43-year-old man from Afghanistan survived with his 14-year-old son, but his wife and his three other children, who were 13, nine, and five did not make it. Another Afghan woman in tears would not move from the beach after losing her husband.
"This is yet another tragedy happening near our shores. It reminds us all that the Mediterranean is a giant mass grave, with tens of thousands of souls in it, and it continues to widen," said Francesco Creazzo, from SOS Méditerranée, an NGO engaged in rescue operations in the central Mediterranean.
"There is no end in sight; in 2013, people said 'never again' to the little white coffins of Lampedusa, in 2015, they said 'never again' in front of the lifeless body of a two-year-old Syrian child on a beach.
"Now the words 'never again' are not even pronounced any more. We only hear 'no more departures', but unfortunately people keep venturing on this journey and they keep dying," he added.