On Friday, it picked up 141 people in two separate operations, half of them children, but it has again struggled to find a port to bring them ashore.
Sophie Beau, president of the vessel's operator SOS Mediterranee, said the ship, which is currently situated between Malta and the Italian island of Lampedusa, had again received "official negative replies" from the two countries.
"We're asking all European countries to find a solution. We're asking them to be responsible and find a safe port in the Mediterranean," she said, accusing Italy and Malta of flouting international maritime law.
Tove Ernst, a spokesman for the European Commission, said it was in contact with "a number of member states that have approached us regarding the incident" to try to find a "swift resolution" to the standoff.
Since June, Italy's new far-right Interior Minister Matteo Salvini has regularly turned away rescue ships operated by foreign NGOs such as the Aquarius, accusing them of playing into the hands of people smugglers.
On Saturday, he said the Aquarius would "never see an Italian port" again.
His hardline stance has sparked a row among EU members, underscoring their failure to come up with a common approach to the influx of people trying to escape conflict, persecution or poverty in Africa and the Middle East.
France, which was within closer range but did not allow the boat access, took in 78 of the migrants after they landed.
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