One person, a 35-year-old woman from Ivory Coast, is known to have died in the shipwreck, and five others including a child are said to be missing.
37 people survived the shipwreck and were disembarked on Lampedusa on Monday night.
They are from Ivory Coast, Gambia, Guinea, Comoro Islands and Cameroon.
Of the group, 16 required medical assistance: 10 for burns and six for hypothermia.
During questioning on Tuesday with the support of cultural mediators, some survivors said they were being towed by a Tunisian trawler but were cut loose when their boat started taking in water.
However, others - the majority - said their boat overturned when a Tunisian fishing vessel drew close in an attempt to steal the engine.
A growing number of boats have been found adrift without an engine in recent weeks.
The rescued migrants and refugees have always reported losing the engine during the crossing.
The survivors of Sunday’s shipwreck were among 829 people to arrive on the tiny Sicilian island on Monday, while 160 people arrived on four boats on Tuesday morning.
ANSA
