The French organization SOS Mediterranee said the ship was carrying 629 migrants picked up in the Mediterranean on Saturday, including 123 unaccompanied minors and seven pregnant women.
The Aquarius had been instructed by the Maritime Rescue Coordination Center in Rome "to transfer 400 of the 629 refugees and migrants now on board back to Italian Navy ships which will then head to Valencia to disembark", MSF Sea tweeted.
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.
Corsican leaders Gilles Simeoni and Jean-Guy Talamoni, the top politicians on the French Mediterranean island, tweeted their offer on Tuesday morning as uncertainty grew over the fate of the 629 people on board the ship.
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Meanwhile, Euronews' correspondent Anelise Borges reported that the situation aboard the Aquarius has deteriorated, with supplies such as blankets and clean clothes starting to run out and fights breaking out amongst the migrants.
Days after assuming office, Mr Salvini issued a warning to people smugglers in a statement that drew direct comparisons with former Australian prime minister Tony Abbott's "stop the boats" rhetoric.
"Turning this into a political weapon is despicable.it is clear that Europe must act more wisely, but we can not let these people die at sea".
By law, it would be hard for Italy to refuse the boat a safe haven, as its own coastguard coordinated the rescues, picking up more than 280 migrants in its own vessels before transferring them to the Aquarius to be taken to safety.
In a statement, the Spanish government said, "It is our duty to help avoid a humanitarian catastrophe and offer "safe harbour" to these people in accordance with worldwide law".
Not everyone in Italy agreed with the government action, and the mayors of a number of southern cities, including Naples, Palermo and Messina, said they would welcome the migrants.
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Malta, for its part, has consistently refused to take in migrants, citing its small size and limited capacities. "The details of this agreement are not known and we don't know if Salvini will inherit that deal", he said.
The diplomatic stand-off had left the migrants stranded at sea and revealed the tough negotiating tactics of Italy's new anti-immigrant government.
"This plan would mean already exhausted rescued people would endure 4 more days travel at sea", Doctors Without Borders said on Twitter.
Under global law, people rescued at sea should be brought to the nearest and safest port for assistance. In two polls conducted in September, 46 percent of Italians said that they felt that migration made Italy less secure, and just over half said that their government had not done enough to curb immigration.
European Union leaders in December set an end-June deadline for an overhaul of rules to create a permanent mechanism to deal with migrants.
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