Meanwhile, hundreds of the migrants aboard the Aquarius were being transferred late Tuesday to two ships operated by the Italian navy and coast guard, which will accompany the rescue ship to the Spanish port of Valencia some 1,500 kilometers (932 miles) away, a journey of some three to four days.
Italy demands an equal share of migrant intake to be distributed across the bloc, something Conte raised at the G7 meeting this past weekend.
The development comes a day after the new Spanish government headed by Socialist Prime Minister Pedro Sanchez offered to allow the Aquarius to dock in Valencia, insisting it was an "obligation" to do so.
The aid group Doctors Without Borders, which operates the Aquarius with SOS Mediterranee, urged both Italy and Malta to reconsider their refusal to allow the stranded migrants landfall and then safe passage by other means to Spain, which has responded to the plight with an offer of safe harbor.
Matteo Salvini, Italy's Interior Minister and Northern League party leader made a decision to refuse docking to "Aquarius" and redirect the vessel to the Island of Malta, apparently in line with his election promises.
"There is a degree of cynicism and irresponsibility in the Italian government's behaviour", said French President Emmanuel Macron through a spokesman.
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The number of migrants arriving in Spain has been on the rise, Benavides reports, while the number of sea arrivals in Italy "has dropped 77 percent compared to this time previous year, following controversial deals with the Libyan Coast Guard and investigations into NGO search-and-rescues".
The aid group said in a statement it had taken "good note" of Mr Salvini's stance, as reported earlier by Italian media.
"My aim is to guarantee a peaceful life for these youths in Africa and for our children in Italy", Mr Salvini said, using a Twitter hashtag which translates to, "We are shutting the ports".
More than 600,000 mostly African migrants have reached Italy by boat from Libya in the past five years.
The outgoing Democratic Party government had already intensified cooperation with Libyan authorities to stop departures and enable Libyan coast guard forces to intercept migrant boats in global waters and take people back to horrific conditions in arbitrary detention in Libya.
However the one-off fix was not adequate, the charity said, calling on European leaders to step up and find shared solutions to support countries on the frontline, such as Italy.
"The people we saved yesterday were in a hard condition, at least 50 were at risk of drowning".
But the decision to close ports was significant because it showed Italy's willingness to put up a stop sign closer to its border.
The 629 passengers - including 123 unaccompanied minors and several pregnant women - had been left in limbo in the Mediterranean since Saturday.