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.
The outgoing Democratic Party government had already intensified cooperation with Libyan authorities to stop departures and enable Libyan coast guard forces to intercept migrant boats in worldwide waters and take people back to horrific conditions in arbitrary detention in Libya.
Meanwhile, the situation with 'Aquarius' was resolved after Spain made a decision to step in following the United Nations refugee agency call to promptly find a way to take the ship full of people in.
The 629 migrants on board include 134 children and seven pregnant women, NGOs operating the boat said.
Italy's new anti-migrant, right-wing interior minister, Matteo Salvini, is making good on a campaign pledge to close Italian ports to non-governmental organizations that pick up migrants at sea, which he has likened to taxi services for migrant smugglers.
It said in a statement that the Aquarius took on the passengers in waters controlled by Libya and where Italian authorities in Rome coordinate search-and-rescue operations.
This would mean already exhausted people rescued have to endure four more days travel at sea.
After Spain's new Prime Minister Pedro Sanchez allowed the ship to dock in Valencia, Salvini celebrated the decision.
"The Mediterranean is the sea of all the countries that face it, and it (Malta) can't imagine that Italy will continue to face this giant phenomenon (of migration) in solitude", the ministers said.
Italy's spat with Malta began after its reported refusal to come to the aid of another rescue ship Seefuchs, which was stranded with 126 migrants on board due to violent seas until it was allowed to dock at the Sicilian port of Pozzallo on Saturday.
Eric Ciotti, a prominent hard-right minister from the Opposition Republicans party, also called on the government to take a tough line on the Aquarius. There are also 21 patients on board who have suffered severe chemical burns after being exposed to a toxic mixture of sea water and fuel for an extended period of time.
But Italy's new anti-establishment government, looking to put pressure on the European Union to rewrite its immigration rules, showed no signs of relenting despite warnings of an approaching storm bringing waves of over two metres.
Italy's new government assumes power at a time when nativist populist parties have growing clout in Europe and its anti-immigrant stance will no doubt be welcomed by Hungary's Viktor Orban, whose government is now trying to criminalize people working for groups that assist asylum seekers. "We need to have an idea of what port to go to, something that up to now we haven't had", Aquarius crew member Alessandro Porro told news channel Sky TG24 on Sunday.
While Spain adopted a diplomatic tone with Italy when it announced it would take the migrants, relations between Rome and Paris have deteriorated in an explosion of accusations and counter-accusations.
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