The agency's special envoy for migrants in the Mediterranean, Vincent Cochetel, underscored that "people are in distress, are running out of provisions and need help quickly".
The French organization said those brought on board included 123 unaccompanied minors, 11 small children and the seven pregnant women.
"Malta is in full conformity with worldwide obligations & will not take the vessel in its ports. France pushes people back at the border, Spain defends its frontier with weapons", Salvini wrote on Facebook.
"This Europe is not showing solidarity", Prime Minister Giuseppe Conte said, adding that "Italy has to deal with the problem" of illegal human trafficking and migration flows "all by itself".
"Italy doesn't shrug off its responsibility when it comes to saving lives, but it asks that others do the same", Transport Minister Danilo Toninelli, in charge of Italian ports and coast guard, said after the Spanish announcement.
Malta's Prime Minsiter Joseph Muscat continued to insist his country is acting according to worldwide law and that it is Italy's duty to take in the migrants, as Italy's coast guard coordinated the rescues off the coast of Libya. However, Malta's Ministry for Home Affairs and National Security issued a statement saying the country is not responsible for the rescue effort coordinated by the Aquarius.
Not everyone in Italy agreed with Salvini's hard line; the mayors of a number of southern cities, including Naples, Palermo and Messina, said they would welcome the migrants.
Speaking to the press in Milan, the deputy PM said: "Evidently raising one's voice politely pays off, something the Italian Government hadn't done in years".
Malta has accused Italy of violating global norms by instructing a migrant rescue ship with 629 people aboard to stay at sea while a diplomatic standoff plays out over where it can dock.
"By closing their ports, Italy and Malta have not only turned their backs on more than 600 desperate and vulnerable people but also on their obligations under worldwide law", Elisa De Pieri, Amnesty International's Italy researcher, said in a statement.
"Our objective is the disembarkation in a port of safety of the 629 people now on board the Aquarius - some we rescued yesterday night in hard conditions", she said.
Sea-Watch said it requested help from the coastguard in Malta to send boats to aid the rescue mission but Malta refused. In particular, Salvini was calling out Malta for being less than thirty miles away and consistently refusing to accept any of these boat people who are rescued at sea.
Salvini has accused the charities of acting as a "taxi service" for the migrants.
Italy's interior ministry were unable to confirm the existence of the letter and said officials were still trying to confirm the existence of the letter.
But Salvini, who channeled Trump last week by telling reporters at a refugee camp in Sicily that Tunisia "isn't exporting gentlemen, it seems more often they're exporting convicts", responded defiantly to calls for mercy, even from the Vatican.