The Open Arms has been anchored since Thursday within swimming distance of Lampedusa and crew say the situation on board is critical after two weeks at sea.
He renewed his constant attacks of recent days on Open Arms, accusing it of lying about the condition of the migrants.
Referring to the migrants' plunge into the sea, Open Arms said in a tweet: "We can not contain the desperation any longer".
Salvini issued a statement on Saturday reiterating that Open Arms could have taken the migrants to Spain and that it was to blame for their plight.
After the charity rejected the plan to go to Algeciras, in southern Spain, the Spanish government offered the captain of the boat the option to dock at the nearest Spanish port, but had not received an answer, the prime minister's office said.
"Spain should first, in its turn, take a step forward and immediately remove its flag from the (charity) ship", Toninelli said in a comment on his Facebook page.
Open Arms, a Spanish-based charity that undertakes sea rescues of those trying to reach Europe as they flee from war, persecution or poverty, accused Salvini of using the 107 migrants for "xenophobic and racist propaganda".
"We are in a state of extreme humanitarian emergency".
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Late on Monday eight migrants that needed urgent assistance and another one accompanying them were evacuated to the Italian port of Lampedusa after being authorized to do so, an Open Arms spokeswoman said. The minors were transferred Saturday to an Italian border patrol boat for disembarkation and processing on the Sicilian island of Lampedusa.
"If your interior minister were to spend some time with those people, listened to their stories, their family traumas, he would change his outlook", the actor said in his Monday interview.
Mr Salvini is eager to capitalise on his soaring popularity and the League's success in May's European elections, when the right-wing party doubled its votes to over 34% from 2018 elections, while the Five Stars nearly halved them to 17%.
European Union states disagree on how to handle the migrants crossing the Mediterranean and some like Italy are taking a tougher position, turning away rescue ships as they seek to dock to drop off rescued people.
Italy's government on Saturday reluctantly agreed to let 27 migrant children from the Open Arms disembark but it required that the rest stay aboard.
Gere said he would like to meet Salvini because "I'm sure he's not like he presents himself in public".
Open Arms founder Oscar Camps on Sunday published a video showing four migrants jumping off the ship in a desperate bid to swim ashore before they were stopped and brought back.
Open Arms, which on Sunday had 107 migrants aboard, has been anchored for days off Lampedusa, a fishing and holiday island between Sicily and northern Africa.
A Norwegian-flagged ship, Ocean Viking, operated by two French humanitarian groups, has been sailing for days with 356 rescued migrants aboard between Malta and Lampedusa and another tiny Italian island, Linosa, awaiting assignment of a safe port. Mr Salvini vowed to block that ship too.