Under the global law, people rescued in the sea should be brought to the closest and safest port for assistance.
Malta's prime minister Joseph Muscat said: "The Italian government is breaching worldwide rules and, with its attitude, is risking to create a situation that would be risky to everyone".
A private rescue ship carrying 629 migrants remained at sea Sunday evening after more than a day of not receiving permission to dock in either Italy or the small Mediterranean island nation of Malta.
The previous Italian government also threatened to close the country's ports last July during last summer's spate of migrant movements across the Mediterranean.
SOS Mediterranee confirmed that there were 629 people on board, including 123 unaccompanied minors, 11 other children and seven pregnant women after being involved in six rescue operations off the coast of Libya.
On Sunday, Salvini said Italy was saying "no to human trafficking, no to the business of illegal immigration".
Maltese Prime Minister Joseph Muscat said Italy's refusal to allow the Aquarius ship to dock at an Italian port risked "creating a unsafe situation for all those involved".
In a stark sign that the city mayors were running against public opinion, the drama over the migrant ship came as the votes were counted for Sunday's Italian local elections in which left-wing, open borders parties show signs of faltering while the populist, anti-mass migration League party stands to make the biggest gains.
Malta is insisting its stand is in line with its worldwide obligations that state any rescued people should be taken to the closest, safest port of call.
The charity added on Twitter: "We have acknowledged what was stated by the Italian interior minister to Italian media".
The Maltese Rescue Coordination Center "is neither the competent nor the coordinating authority", the statement said.
One Aquarius crew member, Alessandro Porro, told Italian news channel Sky TG24 that they desperately needed to know which port to go to.
The charity's spokesperson, Mathilde Auvillain, said the ship had received orders to head north and was now awaiting "definitive instructions".
SOS Mediterranee said Maltese search-and-rescue authorities were contacted by their Italian counterparts "to find the best solution for the well-being and safety" of the people on the ship.
Mr Salvini says he is considering action against organisations rescuing migrants at sea.
Italy has had to deal with hundreds of thousands of migrants in recent years coming via Libya to reach Europe.
Italy's new interior minister has refused to let 600 migrants disembark in Italy, leaving rescue ship in limbo in Mediterranean.
The United Nations estimates that at least 500 people have died in 2018 trying to cross the central Mediterranean, following some 2853 fatalities previous year.