The 629 migrants, including 11 children and seven pregnant women, have been drifting in the central Mediterranean aboard the Aquarius rescue ship since Sunday, when both Italy and Malta shut their ports to it.
Spanish socialist Prime Minister Pedro Sanchez offered to allow the Aquarius to dock in Valencia, insisting it was an "obligation" to do so. "To politely raise one's voice pays off", Salvini told a news conference in Milan.
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.
Conte said that Italy has sent two patrol ships with doctors on board "ready to intervene and ensure the health of anyone on board the Aquarius who might have the need". Malta refused, and when Italy instructed the ship to stay at sea, Malta accused Italy of violating worldwide norms.
Salvini said Malta should disembark the migrants.
Anelise praised the teams of staff on the vessel: "The teams here are very calm, they say the situation is under control and we continue heading north towards the east part of Malta and towards Italy".
It was "essential that the European Union does not look the other way and on the question of migration it is turning away on many occasions", she said.
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In a statement, the Office of the Prime Minister said that the two leaders had discussed the current migration situation and that there was convergence in the two countries' policies.
Pictures issued by SOS Mediterranee showed hundreds of Africans huddled aboard, including a young girl wrapped in a blanket in the arms of a rescue worker. After urging a quick resolution of the impasse earlier in the day, the United Nations refugee agency, through spokesman Charlie Yaxley, said Sanchez's offer "is a welcome development and a great display of solidarity from Spain with refugees".
Naples mayor Luigi de Magistris said on Twitter that "if a minister without a heart leaves pregnant women, children, old people, human beings to die, the port of Naples is ready to welcome them".
Italy's Prime Minister Giuseppe Conte said his country had "asked for a gesture of solidarity from Europe and this gesture has been made".
In a Facebook post dated April 21 a year ago, M5S leader Luigi Di Maio called boats carrying stranded migrants to Italy a "sea taxi", claiming they were conducting services they said were charitable in exchange for money. Earlier in the day, the European Commission had urged action.
"We are talking about people".
The migrants had been rescued from flimsy smugglers' boats in the Mediterranean during a series of operations on Saturday by Italian maritime ships, cargo vessels and the Aquarius itself.
Both Italy and Malta had come under increasing worldwide pressure to allow the migrant rescue ship to dock, and they continued to argue over who was responsible.