The row has triggered global concern about the migrants' plight.
Salvini's nationalist Lega party has promised to expel the 600,000 undocumented immigrants who have arrived in Italy since 2014, mostly from Africa, but he was only able to close the country's ports with the support of his coalition partners in the populist Five Star Movement, which leads Italy's new coalition government.
SOS Mediterranee director general Sophie Beau said Spain's offer "is encouraging and shows that some states are sensitive to the humanitarian emergency".
The migrants will be taken by the Italian coast guard to Spain, but it is not yet clear if they will be taken there directly, or how the rest of the 629 will reach the Spanish mainland.
Spanish journalists on board the rescue vessel have reported the increasingly desperate plight of the migrants over the past 24 hours.
"The International Convention for the Safety of Life at Sea dictates that any ship learning of distress at sea must assist regardless of the circumstances".
Malta and Italy both thanked Spain for stepping up, but maintained their dispute over who was responsible.
On Sunday, Maltese Prime Minister Joseph Muscat accused Italy of "violating worldwide law" for implementing a similar policy. "We will have to sit down and discuss how to prevent this from happening again", he added. "This is a European issue".
In an attempt to ease the stalemate, a number of mayors of port cities in Italy on Monday said that they would allow the ship to dock in their cities.
"That's why we ask the government in Valletta to take in the Aquarius in order to offer first aid to the migrants on board".
The EU and the bloc's biggest member state Germany made similar pleas.
The conversation came at the end of a day when the rescue vessel Aquarius was denied entry into both Italy and Malta reportedly as a result of a dispute between the two countries.
Salvini refused to back down.
The Italian government responded with a statement saying "Italy can not accept hypocritical lessons from countries that in the migration field have always preferred to turn their head to the other side", Italian media reported, adding that Rome is considering canceling a summit between Macron and Italian Prime Minister Giuseppe Conte on Friday. "Italy has stopped bowing its head and obeying, this time THERE IS SOMEONE WHO SAYS NO. #chiudiamoiporti (#weareclosingtheports)", Salvini wrote on Twitter, as quoted by the Ansa news agency.
The ship was heading for the Italian port of Messina Sunday when Italian officials ordered it to stop and remain in place, 27 miles west of Malta and 35 miles south west of mainland Italy.
The migrants were rescued in six separate night-time operations in the central Mediterranean on Saturday.
Calling for immediate disemarkation for the 629 people, including 11 children and seven pregnant women, MSF said the better option would be to disembark in the nearest port, after which the refugees can be transferred to Spain or other safe countries for further care and legal processing.
But critics have increasingly accused the group of actively encouraging migrant crossings, since those leaving Libya know there is a good chance they will be rescued.
The passengers, with many migrants from Sudan among them, were apparently unaware of they had become pawns of sorts in Europe's new political equilibrium.
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The film stars Colin Farrell , Danny DeVito , Eva Green and Michael Keaton , plus newcomers Finley Hobbins and Nico Parker . It's also a surprising departure for Burton, whose name has become synonymous with a Gothic flair and kabuki-mask faces.
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Shams Charania , an insider for Yahoo! According to a report from Jonathan Givony , Doncic will indeed remain in the draft. If the Suns do hang on to the No. 1 pick, it's expected that they'll select the seven-foot, 260-pound Ayton.
Trump and Kim signed an agreement to work toward denuclearization, but it appears weaker than past deals that failed. Mr Trump made the announcement following his summit with North Korean leader Kim Jong-un in Singapore on Tuesday.
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Huge Dust Storm Strikes NASA’s Opportunity Rover
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Intel will be releasing its first discrete GPU in 2020
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Proposal to split California into 3 states goes to ballot
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Australian tourist dies 'while trying to take selfie'
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Seeyouatmidnight to serve the Scots a Grand National double
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But even so, there’s no denying that he has impressive skills and he managed to lead all his football teams to big titles. Now at PSG, there are a lot of rumors that he might come back in Spain to play for life-time rivals of Barcelona, Real Madrid.