At least three people were killed after the explosion, which was likely caused by a gas leak, said authorities, who have opened an investigation.
Italy’s former interior minister Matteo Salvini was present for the opening day of the trial for his actions preventing migrant landings in Sicily in 2019.
Europe continues to struggle with some of the worst wildfires the region has seen in decades.
The Italian island of Lampedusa is one of the main landing points on the route for migrants departing mostly from Tunisia and Libya to reach Europe.
The people aboard were "in serious psycho-physical conditions that make it impossible for them to stay on the petrol tanker", Mediterranea said after the transfer.
Novel coronavirus has infected more than 6.4 million people around the world. Here are pandemic-related updates for June 2:
Mexican drug cartels are distributing food and hand sanitiser as residents struggle because of the pandemic, while in Italy Mafia gangs are offering loans to the poor.
Italy could be facing a significant loss of jobs, business closures and international isolation.
The boat, which survivors said had departed from Libya taking advantage of a respite in bad weather, was believed to be carrying some 170 people.
Italian coastguard says it recovered bodies of 13 women, some of them pregnant, after a small overloaded boat carrying around 50 migrants capsized off Lampedusa.
More than 100 migrants stranded off the Italian coast cannot find a home, as Italy refuses to let them ashore until EU states offer them sanctuary.
More than 200 police, including officers from the US Federal Bureau of Investigation (FBI), have been carrying out 19 arrest warrants since dawn targeting the Inzerillo clan in Sicily's capital Palermo and the New York-based Gambino family.
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