Transport Minister Danilo Toninelli, who is nominally in charge of the ports, said: "Malta can not continue looking the other way when it comes to respecting worldwide conventions".
The charity said the group of mainly sub-Saharan Africans were picked up in six different rescue operations off the coast of Libya and included hundreds who were plucked from the sea by Italian naval units and then transferred to The Aquarius.
Italy's firebrand interior minister, Matteo Salvini, who leads the anti-immigrant League party in the governing coalition, has long railed against what he depicts as Europe's failure to show solidarity with Italy during the migrant crisis in recent years.
"From today, Italy will also start to say no to human trafficking, no to the business of illegal immigration".
Some 629 people, including pregnant women and scores of children, were saved by SOS Mediterranean on Saturday and are stuck aboard the French NGO's ship Aquarius, which is now between Malta and Sicily waiting for a secure port. "But Italy has stopped bending its head and obeying".
"Salvini is violating the global law".
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Italy's former ambassador to Malta has urged the two countries to tone down their rhetoric and seek a common solution to the fate of the Aquarius migrant ship.
The Maltese authorities have been insisting that since the rescue happened in the Libyan search and rescue area and was coordinated from Rome, Malta is neither the coordinating authority nor has the competence to settle this issue, thus it would not take in the migrants and asylum seekers. The Rome-based rescue coordination centre gave the instructions.
"The boat is now heading north towards a secure port", SOS Mediterranee tweeted on Sunday without specifying its destination, though virtually every such boat over the past five years has ended up in Italy.
One Aquarius crew member, Alessandro Porro, told Italian news channel Sky TG24 that they desperately needed to know which port to go to.
The same day Italian authorities held the migrant rescue boat Sea-Watch 3 for 12 hours after it brought 232 people to Reggio Calabria, on the south-western tip of the mainland. Right-wing politicians have accused charity boats operating off the coast of Libya of operating as "taxis" for migrants.
The small island nation with fewer than a half million inhabitants says it already accepts more refugees per capita than Italy, which has taken in more than 600,000 boat migrants since 2014.
The United Nations estimates at least 500 people have died in 2018 trying to cross the central Mediterranean, following more than 2,800 fatalities previous year.