The rescue ship's crew pulled 229 migrants from the water or from traffickers' un-seaworthy boats on Saturday night, including 123 unaccompanied minors and seven pregnant women.
The Aquarius had been heading to Sicily after rescuing migrants off the Libyan coast, but Mr. Salvini, who is also interior minister and deputy prime minister, said that all Italian ports would be closed to it and other rescue ships.
"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.
Barcelona's mayor Ada Colau also offered to welcome the ship, arguing that saving human lives should be prioritised.
The charities said the migrants were picked up in six different rescue operations and that hundreds of them had been delivered to the Aquarius by Italian navy ships that were patrolling the waters off Libya.
Matteo Salvini, Italy's Interior Minister and Northern League party leader chose to refuse docking to "Aquarius" and redirect the vessel to the Island of Malta, apparently in line with his election promises. The Aquarius, which was built in 1977 as a German coast guard ship, has 629 migrants on board, mainly from sub-Saharan Africa.
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. Italy demanded that Malta take in the migrants, arguing that the island was the closest safe port, but Malta accused Italy of breaching its worldwide obligations.
More than 600,000 mostly African migrants have reached Italy by boat from Libya in the past five years.
Satisfied with Spain's offer, Salvini later told reporters the standoff with Malta was "an important first signal" that Italy would no longer tolerate being left alone to accept and process would-be refugees.
The migrant influx has led to a populist backlash, with Salvini vowing to prevent Italy from becoming the "refugee camp of Europe".
However, it is now unclear whether such a move is possible as the Aquarius is obliged to obey the commands of the Maritime Rescue Coordination Center (MRCC), an arm of the government-controlled Italian Coast Guard.
"Nevertheless I am very anxious for the direction taken by Italian authorities". But at the same time, the responses of other nations in the region seem to support what Italy's Interior Minister is saying. "This time there's someone saying no".
Sea-Watch said it requested help from the coastguard in Malta to send boats to aid the rescue mission but Malta refused.
For years the European Union has largely ignored Italy's rising fury at being left to deal with the migration crisis (even when it came from more politically acceptable figures like Matteo Renzi) but with Mr Salvini in charge, that may no longer be possible.