In a statement the Maltese government said the rescue made by the Aquarius took place off the Libyan coast, closer to Libya, Tunisia and Italy (Lampedusa) in an operation which was coordinated by the Libyan authorities.
The group said many reported they had been held in inhumane conditions in Libya.
The vessel, which is jointly operated by MSF and SOS Mediterranee, is understood to have rescued the migrants on Friday.
"What is of utmost importance is that the survivors are brought to a place of safety without delay, where their basic needs can be met and where they can be protected from abuse", said the group's search and rescue coordinator, Nick Romaniuk.
Due to pressure from Italy and Malta, most charity ships are no longer patrolling off the coast of Libya.
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He said Iran needed to make tangible and sustained changes to behave like a normal country. He added, "America is turning up the pressure and we want the United Kingdom by our side".
The Aquarius is a former German Coast Guard vessel that is now registered in Gibraltar - a British Overseas Territory to the south of Spain.
She said "it could of course be the case that in theory a flag state of a rescue ship could be considered a potential location for disembarkation, but this might not be possible in practice".
He says the migrants were given humanitarian and medical aid, and were taken back to the Libyan town to a refugee camp.
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 migrants will be brought to Malta in the afternoon, sources said.
Cargo and other commercial vessels often have plucked migrants to safety from deflating rubber dinghies and rickety wooden boats. Recently a support ship for an offshore oil platform was left in limbo for days after rescuing migrants.
"People rescued in the worldwide waters of the Mediterranean must not be returned to Libya, but should be taken to a place of safety in line with global and maritime law", MSF said in a statement, saying that numerous migrants had suffered abuse during their transit through Libya. "It was extremely fortunate that we spotted these boats in distress ourselves". Traffickers have exploited Libya's chaos after the 2011 uprising that toppled and later killed longtime ruler Moammar Gadhafi.