Maltese Prime Minister Joseph Muscat said Italy's refusal to allow the Aquarius ship to dock at an Italian port risked "creating a unsafe situation for all those involved".
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".
Mr Salvini is being seen as making good on "get-tough" anti-immigration electoral promises by banning the boat Aquarius in a move which has seismic implications for the European Union and its immigration policy.
The Aquarius and its passengers were caught up in a crackdown swiftly implemented by the right-wing partner in Italy's new populist government, which has vowed to stop the country from becoming the "refugee camp of Europe".
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"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. The trip would take four to five days, and with so many people aboard the boat and bad weather making seafaring conditions hard, going to Valencia would be "a insane idea".
A doctor on the ship, Dr. David Beversluis, said there were no medical emergencies onboard but one passenger had to be revived after he was rescued.
Drama over Salvini's closed ports policy intensified Monday morning as a second migrant ship bound for Italy and presently in Libyan waters, having collected its human cargo, was also blocked by the government. "Malta takes in nobody", Salvini wrote on Facebook. While the details of that agreement were not made public, Salvini told Russians at the time that his goal was to work "so that Italy has real parliamentary elections, just as open as in your country". 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.
A migrant rests on the deck of the MV Aquarius as it sails into the Sicilian port of Messina, on May 14, 2018.
Another local resident, Natale Lombardo, said illegal migrants disembarking on the island were virtually "invading" them, adding that "he who arrives here legally is welcomed, but between these people there are also illegals and those can't be tolerated".
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In the meantime some in Italy have offered to take in the migrants, with the mayor of Taranto, Rinaldo Melucci, saying that the Calabrian port city was "ready to embrace every life in danger".
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. "We need to have an idea of what port to go to, something that up to now we haven't had".
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.
Last week, Salvini said Rome should increase its deportations of migrants.
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