Italy's interior minister told more foreign non-government organisations operating migrant rescue ships in the Mediterranean on Saturday that they could not dock in Italian ports and blasted one of them for calling him a fascist.
The Aquarius itself is due to dock once all the migrants are off the Italian vessel.
The Aquarius, operated by Doctors Without Borders, pulled into the port of Valencia. It took the convoy almost a week to travel the 1,500 kilometers (930 miles) between Sicily and Spain.
Noguera said more needs to be done to find better solutions for the migrant and refugee issues that European countries are facing. "I am happy that the journey is over, a journey that was too long, and I am anxious for the situation in the Mediterranean and the closing of European ports".
The migrants were met by emergency workers, including health officials and psychologists, at the city's marina. Each were assigned to a translator and authorities worked to determine their identities before they were sent to welcome centers.
The plight of the Aquarius has again highlighted the failure of European Union member states to work together to deal with the influx of migrant arrivals since 2015.
After the first boat docked, medical staff wearing white overalls, gloves and masks went on board to carry out initial medical checks before the migrants disembarked in groups of 20.
Anti-migrant feeling has surged in Italy as more than 600,000 people have arrived on its shores over the past five years, helping to propel the nationalist League into a coalition government.
"We have to strike a balance between our sensibilities and humanity, and our respect for the law", said Spain's migration minister, Magdalena Valerio.
No serious illness was reported among the migrants, who included seven pregnant women and 123 minors, but many had suffered burns and fatigue.
The U.S. 6th Fleet said the migrants rescued by its fast transport ship on June 12 were moved to the Italian ships on Sunday near tiny Lampedusa. A private aid ship said it couldn't assume the unexpected passengers from Trenton because Italy wasn't assigning it a port within its navigational capacity.
There are now 106 migrants on the vessel, after two ships from Italy's coast guard and navy shared out the passengers to make the long journey safer.
Spanish Prime Minister Pedro Sanchez, with a more liberal stance, said the country would offer a safe harbor.
"We were aware that something "exceptional" could happen since the Aquarius had left to rescue migrants, but we never thought of something like this", Corral said.
The first of three vessels entered Harbour soon after dawn. In practice, the policy has placed a heavy burden on Italy and Greece, where hundreds of thousands of asylum-seekers have arrived in recent years.
Spain offers universal healthcare to its citizens, though the former centre-right government withdrew the right to general healthcare for undocumented migrants in 2012, as part of a programme to cut spending.