The aid group said in a statement it had taken "good note" of Salvini's stance, as reported earlier by Italian media.
Malta's government replied to the statement saying Prime Minister Joseph Muscat had spoken to Italian premier Giuseppe Conte, and underlined "that Malta is acting in full conformity with its global obligations".
Despite the claim by Mayor Orlando that the government stands in opposition to worldwide law by closing the ports to migrant smuggling operations, a distinguished expert on global maritime law Admiral Paolo Caffio has given his verdict, stating that not only is it legal, but there is also precedent, reports Il Giornale.
Mr Salvini said on Sunday Italy was saying "no to human trafficking, no to the business of illegal immigration".
Salvini pointed to Malta's unwillingness in accusing Europe as a whole of leaving Italy on its own to deal with the refugee crisis.
In a statement late Sunday after speaking with his Italian counterpart, Muscat refused to let the ship dock in a Maltese port, but said Malta will conduct emergency medical evacuations if necessary. "But Italy has stopped bending its head and obeying".
The migrants had been rescued during a series of operations on Saturday by Italian maritime ships, cargo vessels and the Aquarius itself.
"My aim is to guarantee a peaceful life for these youths in Africa and for our children in Italy", Mr Salvini said, using a Twitter hashtag which translates to, "We are shutting the ports".
As of Monday morning, the Aquarius was circling in worldwide waters off Malta after the Italian maritime coordination centre in Rome ordered the vessel to stay put (see map).
"I am very sorry to see what's going on between Malta and Italy, with exaggerated tones from both sides, unsubstantiated allegations flying about, and threats of "retaliation" such as cutting off Malta's electricity supply", Giamberto de Vito said on Facebook.
There was no comment from the Italian Ministry of the Interior or the local coastguard.
The Maltese Rescue Coordination Center "is neither the competent nor the coordinating authority", the statement said.
The group said it "urgently requests a swift resolution and a designated port of safety". We have always welcomed rescue boats and vessels who saved lives at sea.
The ship Aquarius, carrying 629 migrants from Libya, including seven pregnant women, is operated by the charities Medecins Sans Frontieres and Sos Mediterranee.
The United Nations says at least 785 migrants have died crossing the sea so far this year.
Salvini says Italy should not be the only country taking in boats arriving from North Africa and urges Malta to allow the ship to disembark.