Mr Salvini also took aim at other European countries that were involved in rescue operations in the Mediterranean but did not actually take in any migrants.
"It is our obligation to help avoid a humanitarian catastrophe and offer "a safe harbor" to these people, thus complying with obligations of global law", he said in a statement. "It is our duty to help avoid a humanitarian catastrophe and offer a "safe harbour" to these people in accordance with worldwide law".
"People are in distress, are running out of provisions and need help quickly".
"I don't think the Italian government can deny a port of safety to the Italian Coast Guard, but they can to a foreign-flagged ship like the Aquarius", he told CNN Monday.
When the Italian government took office last month, the big fear in Brussels was that it would use a threat to withdraw from the euro currency as a way to get what it wanted in Brussels.
"It's recognition that Italy can't continue to endure this huge burden alone, " Salvini said at a news conference.
"Italy has stopped bowing our heads and obeying", Salvini said in a Facebook post.
The Maltese government insisted it was "acting in full conformity with its global obligations".
A handout photo made available by SOS Mediterranee shows the sea rescue of a total of 629 migrants.
Under global law, people rescued at sea should be brought to the nearest and safest port for assistance.
As such Malta will not take the said vessel in its ports.
But the Spanish ports may be too far away for the overburdened Aquarius. The vessel with 123 unaccompanied minors and seven pregnant women on board is stranded in the Mediterranean Sea. "This time we say no", Mr Salvini said, urging Malta, to accept the ship.
Themis' operational area will span the Central Mediterranean Sea from waters covering flows from Algeria, Tunisia, Libya, Egypt, Turkey and Albania.
"The people we saved yesterday were in a hard condition, at least 50 were at risk of drowning".
The migrant rescue charity SOS Méditerranée, which runs the Aquarius, said 629 migrants had been picked up in six different rescue operations off Libya's coast on Sunday.
The country refuses to take in migrants because of its small size. Italy is the entry point for migrants from North Africa going to Europe.
Italy has been the de facto destination for rescue boats since the migrant crisis began five years ago.
But the political mood in Italy has changed, with resentment growing among voters toward both migrants and the European Union.
In an attempt to ease the stalemate, a number of mayors of port cities in Italy on Monday said that they would allow the ship to dock in their cities. "We need to know who is arriving", a local man, Salvo Cavallaro said, "these 600 people, we don't know who they are".