Malta said no too, exposing deep divisions over undocumented migrants fleeing to Europe.
Italy's new populist government and Malta refused to let the ship dock in their ports, accusing each other of failing to meet their humanitarian and European Union commitments.
The migrants, majority from Africa, were welcomed by a team of more than 2,000 people, including 470 translators and 1,000 Red Cross volunteers who distributed basic items such as blankets, clothes and hygiene kits.
Referring to the costs, Salvini added: "Seeing that we pay, we'll take in who deserves to be taken in".
Germany took in more than a million refugees and migrants in 2015-2016, mostly from Syria, Iraq and Afghanistan.
Pope Francis says that the Gospel teaches that it's wrong to leave migrants "at the mercy of the waves", an apparent critique of Italy's new migration policies.
Spain yesterday said it has accepted an offer from France to take in migrants from a rescue ship following a turbulent week surrounding the stricken vessel.
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.
Muscat also called for an immediate thawing in diplomatic relations between Malta and Italy, arguing that Malta welcomes Italians seeking work here with open arms. It is due to arrive in Valencia on Sunday.
But just two weeks before the self-imposed deadline of the June 28-29 EU summit in Brussels, EU countries remain deadlocked on how to relocate asylum seekers in the event of a new crisis.
In Rome, thousands of people protested against Italy's anti-migrant policies, as they demanded the government find a more humane solution to an issue which has divided Europe. Monica Oltra, left wing vice president of the Valencia regional government, said, "The Mediterranean Sea must not become a mass grave".
"I felt emotional when I saw posts on social media by the Italian community in Malta saying that Malta acted correctly [in the Aquarius case] and calling Malta their new home", he said. Spanish officials plan to do a case-by-case analysis of the migrants' requests for asylum.
The refusal by Italy and Malta to allow the Aquarius to dock has reignited a continentwide battle over how to handle immigration. The trip to the Spanish port took almost a week.
The rescue ship Aquarius and another Italian navy ship, the Orione, will arrive in the coming hours, discharging 630 migrants in all.
Mr Salvini has warned that other rescue ships would also be banned from docking in Italy. Spain ended up offering the ship safe harbour. It took the convoy almost a week to travel the 1,500 kilometers (930 miles) between Sicily and Spain.
All the other rescues happened in the Alboran Sea, between northeastern Morocco and southeastern Spain.
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. The journey to Valencia took almost a week.
Salvini, leader of the anti-immigrant League, lost no time in falling out with some close European allies over his decision to deny access to port for a refugee vessel earlier this month.
The boat operated by aid groups SOS Mediterranee Sea and Doctors Without Borders touched land shortly before 11am Sunday with 106 migrants on board.
After Spain offered to take in the survivors, the ship started an 800-mile journey to Valencia along with two Italian ships, which were sent to ease the overcrowding.
The migrants were met by emergency workers (pictured bottom right) including health officials and psychologists, at the city's marina.
Among the passengers are 450 men and 80 women - at least seven of them pregnant - as well as 89 adolescents and 11 children under the age of 13, figures released by the Valencian authorities show.
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