"There were 13 dead. Some people were saved and sent to nearby hospitals," Franco Susino, the mayor of Scicli in southeast Sicily near where the incident happened, said on news channel SkyTG24.
"We did what we could to save human lives. Some tourists raised the alarm and helped out," he said, adding that he believed the refugees had been thrown overboard by crew members.
"These people are treated like animals," he said.
SkyTG24 and the ANSA news agency said there were between 150 and 200 people packed on the boat and Susino said most of them were from Eritrea.
Ansa said two suspected crew members have been arrested under an Italian law against people who facilitate illegal immigration.
In a similar incident in Catania in another part of Sicily in August, six young Egyptians drowned trying to reach the shore.