The Aquarius - run by SOS Mediterranee and Doctors without Borders (MSF) - rescued 141 people in two separate operations off the Libyan coast on Friday.
Sophie Beau, president of the vessel's French operator SOS Mediterranee, said the ship, now at sea between Malta and the Italian island of Lampedusa, had again received "official negative replies" from the two countries.
Of the rescued people, 25 are thought to have spent 35 hours adrift at sea.
More than 70 per cent of those rescued originate from Somalia and Eritrea.
The group said many reported they had been held in inhumane conditions in Libya.
The migrant rescue vessel, MV Aquarius is extremely unlikely to dock in Gibraltar, even though it is registered here, GBC understands.
Italy has demanded Britain take in 141 migrants rescued by a ship that flies under the flag of Gibraltar. "Ships might be unwilling to respond to those in distress due to the high risk of being stranded and denied a place of safety", Vimard said.
Doctors Without Borders said numerous people who were rescued are weak and malnourished.
Though departures from Libya have fallen dramatically this year, people smugglers are still pushing some boats out to sea.
Malta was neither the coordinating nor the competent authority for such a rescue, and therefore has no legal obligation to make the arrangements to provide for a place of safety.
Italy and Malta have both refused permission for the Aquarius to enter harbour and disembark some 140 migrants picked up at sea.
The people rescued told the crew that several ships passed them by without offering assistance, according to SOS Mediterranee. The ship is now anchored between Malta and Italy. The migrants will be brought to Malta in the afternoon, sources said.
The Aquarius' search and rescue coordinator Nick Romaniuk said some migrants on board were sick and wounded and "need to be disembarked as soon as possible" for proper medical care.
More than 650,000 migrants have come to Italy's shores since 2014, prompting Rome to accuse its European Union peers of not sharing the burden of caring for those who arrive on the bloc's southern border.
"We're asking all European countries to find a solution".
The criminalisation and obstruction of humanitarian organisations reflects the larger problem of a broken European asylum system and the failure of the EU member states to relocate asylum seekers who arrive in Europe. People rescued in the global waters of the Mediterranean must not be returned to Libya, but should be taken to a place of safety in line with worldwide and maritime law.