The 67 migrants – including women and children – stuck on the Diciotti at the port in Trapani are at the centre of a row after a handful reportedly revolted after their rescue amid fears that they would be returned to Libya.
"I am not giving permission to anyone to disembark from Diciotti: if anyone does so, they will take responsibility for it," said Salvini on the sidelines of a summit with his European counterparts in Austria.
Initially picked up by a supply vessel, the Vos Thalassa, over the weekend, the migrants were subsequently transferred to a coastguard ship after staff made emergency calls to authorities in Rome.
According to Italian media, sailors aboard the Vos Thalassa locked themselves in the control room and called for help after two migrants with mobile phones and GPS realised that the boat was heading south back towards Libya, sparking a furious reaction from some on board.
Migrants trying to reach Europe are desperate not to be returned to Libya, where they face abuse and rape in detention centres.
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"If there was violence [on board the Vos Thalassa], the perpetrators will go to prison and if there was no violence, because someone lied, then they [those who supposedly lied] will suffer the consequences," Salvini – who is also the leader of the hard-right League party – said.
The Diciotti will be blocked "for as long as necessary" to clarify the situation, Salvini added.
The nationalist minister – who has authority over Italian ports – initially refused to allow the Diciotti to dock in Italy, despite previously saying that ports would remain open for Italian naval and coastguard ships carrying migrants.
Salvini has banned charity rescue boats operating in the Mediterranean from docking in Italy, accusing them of aiding human traffickers to bring migrants to Europe.
The latest tussle over migrant arrivals comes as 28 interior ministers meet in the Austrian city of Innsbruck for a summit focused on finding a common migration plan as tensions over the contentious issue rise in Europe.
The case of the Diciotti has also highlighted a split within Italy's government coalition, which includes the League and Luigi Di Maio's Five Star Movement, whose left fringe is opposed to the closing of Italian ports.