As many as 986 people were rescued at sea and four died in the past 48 hours as they made their way from North Africa to the Straits of Gibraltar and Spain's western Mediterranean coast, the Spanish maritime rescue service said on Saturday.
Chartered by a French aid organisation, the rescue vessel took in 629 migrants including many children and pregnant women off Libya's coast last weekend.
Italian Premier Giuseppe Conte says Italy is working on a proposal for a "radical paradigm change" in the way Europe manages migration that focuses on the countries of migrants' origin and transit. Majority from Africa but others are from Afghanistan, Pakistan and Bangladesh, according to medical charity Médecins Sans Frontières.
The statement said Spanish Prime Minister Pedro Sanchez "appreciated the cooperation of (French) President (Emmanuel) Macron and believes this is the framework of cooperation that Europe should use to respond" to immigration on the continent.
The arrival came after Spain's Foreign Minister Josep Borrell agreed the migrants could go there "to oblige Europe to forge a common policy to a common problem".
The Aquarius and two Italian ships carrying the migrants are expected to arrive at Spain's eastern port of Valencia on Sunday.
The ship was held for two days between Malta and the Italian island of Sicily after the latter nation's Interior Minister, Matteo Salvini, refused to allow it to dock.
Macron's office said the discussions will focus on migrant-related issues and other major European topics ahead of an EU summit at the end of the month.
All the migrants will get special 45-day humanitarian permits to stay, and asylum requests will be assessed, Spain has said.
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Carmen Moreno, a doctor and Red Cross volunteer who helped look after the migrants after they disembarked, said they were "very excited and hopeful".
Migrants are seen after being rescued by MV Aquarius, a search and rescue ship run in partnership between SOS Mediterranee and Medecins Sans Frontieres in the central Mediterranean Sea, June 12, 2018.
Spanish police say the migrants arriving on the Aquarius convoy will be granted 45 days before they must start to resolve their legal situation in Europe.
Spain has accepted the French government's offer to take in those migrants who want to go to France "once they have fulfilled the protocols".
After the Aquarius docked, aid workers cheered as migrants walked off the ship, the Associated Press reports.
He said his ship was too small to make the journey from Libya to Italian ports and that he always transferred migrants to other ships, but insisted those craft should have the right to land in Italy.
After Rome's decision to ban the Aquarius, Macron and Italian Prime Minister Giuseppe Conte met on Friday and agreed that the European Union should set up asylum processing centres in Africa to prevent "voyages of death".
Had Malta been the closest port of call, and thus duty-bound to take in the migrants aboard the Aquarius, Malta would not have hesitated to do so, Prime Minister Joseph Muscat said on Sunday. "As minister and as a father, I take this action for the benefit of all".
An Italian coast guard ship had already arrived in Valencia with 270 of the 630 total migrants that the Aquarius saved off Libyan shores over a week ago.