The migrants saved by the Aquarius, run by French NGO SOS Mediterranee, were stuck on the overloaded ship for over 30 hours as Italy and Malta bickered over who should take them before Spain stepped in and offered the port in Valencia as a place for the migrants to land in Europe.
The first group of migrants have been transferred from the humanitarian ship Aquarius - which had rescued 629 migrants crossing from Libya - to an Italian coast guard vessel, reports say.
Representatives from Italy, Malta, Cyprus and Greece agreed at a meeting Monday with the Hague-based International Commission on Missing Persons to increase information sharing and cooperate more in investigations into migrants who never make it to Europe.
The ship, which is severely overloaded, is operated by SOS Méditerranée and Médecins Sans Frontières (MSF).
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Italian Premier Giuseppe Conte said he personally contacted Malta's prime minister, Joseph Muscat, to "explicitly at least take on the human assistance of persons in difficulty aboard the Aquarius".
Italy's hardline immigration policy under its new populist government could have knock-on effects in neighbouring France, where President Emmanuel Macron has also tightened immigration laws to crack down on illegal arrivals.
Malta has accused Italy of violating worldwide norms by instructing a migrant rescue ship with 629 people aboard to stay at sea while a diplomatic standoff plays out over where it can dock.
"No one should dare brand Italy or its government as inhumane or xenophobic", Transport Minister Danilo Toninelli told Radio Capital.
Its route north will take it past Malta, and the Italian government said its port authorities had written to the small island state asking it to let the Aquarius dock there.
"Why do 629 people on Aquarius still have to suffer?"
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Athens officials had objected to the name Macedonia , fearing territorial claims on a northern Greek province of the same name. Ever since the Republic of Macedonia declared its independence in 1991, Greece has been fighting the country over its name.
Malta said Italy co-ordinated the rescues and that it has had nothing to do with it.
Earlier in the day, the Maltese government also refused to accept migrants from the Acquarius.
Salvini's League scored its best-ever result in March national elections, partly on pledges to deport hundreds of thousands of migrants and halt the flow of newcomers, and has formed a coalition with the anti-system 5-Star Movement.
Malta's prime minister, who had resisted Italian pressure to take the migrants, thanked Spain's new government for defusing the crisis.
The regional leader of Spain's Basque Country, Inigo Urkullu, said the region was prepared to take care of 10 percent of the passengers.
"You can't create a precedent that will enable one European country to offload onto other European countries", he continued. On Sunday evening, he posted an image of himself on Twitter with his arms crossed above the message, "We are closing the ports", rendered as an Italian hashtag. Merchant vessels have diverted from their commercial voyages to rescue more than 50,000 people in the Mediterranean since 2015. On Monday afternoon, Spain offered to take the ship.
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The Selecao superstar moved to 55 goals in 85 caps, equaling the record of 1994 World Cup victor Romario. However, he was a different player in Vienna and managed to score his 10th goal in 17 games for Brazil .