The shipwreck took place near Steccato di Cutro, a seaside resort on the eastern coast of Calabria, the region that forms the tip of Italy's boot.
The death toll "has surpassed 30", Danilo Maida, spokesman for the Italian firefighters' service in Calabria told Reuters on Sunday, adding that the count was provisional.
Firefighters and other emergency services were looking for more survivors at sea using jet skis, but conditions were harsh, making the search difficult, he added.
Earlier, Italian news agency ANSA reported that 27 bodies were found on the beach, and more bodies were spotted at sea.
Italian Interior Minister Matteo Piantedosi called it a tragedy and said migrant sea crossings must be stopped.
"It is a huge tragedy which shows the absolute need to act firmly against irregular migration channels," Mr Piantedosi said in a statement.
It is "essential" to stop sea crossings which, offering migrants the "illusory mirage of a better life" in Europe, enrich traffickers and "cause tragedies like today's", he added.
On their official Telegram channel, firefighters said they had recovered 28 bodies, and indicated the migrants' ship had ran aground by the coast.
The Adnkronos news agency said more than 100 people were aboard the ship, while AGI, another Italian news agency, said a baby and several children were among the dead.
The vessel, bringing migrants from Iran, Pakistan and Afghanistan, crashed against rocks during rough sea weather, Adnkronos said.
Italy is one of the main landing points for migrants trying to enter Europe by sea. The so-called central Mediterranean route is known as one of the world's most dangerous.
According to the International Organisation for Migration's Missing Migrants Project, 20,333 people have died or gone missing in the central Mediterranean since 2014.
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