On Tuesday morning, Italian rescuers offered to help transfer the migrants to Spain, following three nights of tension for the migrants and aid workers, and after authorities on the French island of Corsica also offered the vessel safe haven.
A little more than a week ago, Italy's new interior minister, Matteo Salvini, told a crowd that "Italy and Sicily can not be Europe's refugee camp" and "the good times for illegals are over", Deutsche Welle reports.
The move also created rifts with Malta's Prime Minister Joseph Muscat who said the he was "worried about the direction taken by the Italian authorities" that according to him went against worldwide law.
But critics have increasingly accused the group of actively encouraging migrant crossings, since those leaving Libya know there is a good chance they will be rescued.
They had hoped to find refuge in Italy.
While Spain's foreign minister said he hoped its gesture of solidarity would help push other European Union members to re-examine migrant policy at a summit later this month, French President Emmanuel Macron criticized Italy's cynicism and irresponsibility for leaving the migrants at sea, while also deflecting criticism for not allowing the ship to dock in France.
But Malta and Italy - whose new populist government has vowed a tough new stance on immigration - have both refused to take the migrants in, triggering concern in the global community about their plight.
More than 600,000 migrants and refugees have reached Italy by boat from Africa in the past five years.
In the meantime, some in Italy have offered to take in the migrants, with the mayor of Taranto, Rinaldo Melucci, saying that the southern port city was "ready to embrace every life in danger".More news: E3 2018: Bethesda Announces Starfield (+trailer)
"Italy can not accept hypocritical lessons from countries that have preferred to look the other way on immigration", the new populist government said in statement initially reported by Italian media and then confirmed by government representatives to AFP.
The migrants were picked up off the Libyan coast at the weekend and were packed onto the Aquarius which is operated by the charities SOS Mediterranee and Medecins san Frontieres.
Matteo Salvini, the leader of the far-right League party, said Malta should take in the ship, the Aquarius, but his request was rejected.
The U.S. Navy has confirmed that one of its ships was involved in a rescue operation in the Mediterranean. The Aquarius, a humanitarian ship run by the NGO SOS Mediterranean and Doctors Without Borders (MSF), said it saved 946 people, including 200 unaccompanied minors rescued after being found drifting on nine wooden and rubber boats.
On Tuesday, France's president and prime minister took the newly-elected government of Italy to task for refusing to grant a migrant rescue vessel permission to dock. In practical terms, no ships of this type will be able to land without cooperation of the Italian coastguard, which is under the direct command of the Italian government.
The NGOs suggested that the hundreds on board "are running out of provisions".
"There are more than 600 people onboard, they are exhausted, they want to get to safety, there is, of course, a lot of tension among them because they are not sure what is going to happen", she added.
But efforts to break the stalemate between Italy and Malta are expected to continue.