SOS Mediterranee in a statement said that because of the recent refusal of Italy and Malta to let rescue vessels carrying migrants dock, ships might be now unwilling to get involved fearing they will be stranded with migrants aboard and denied a port to disembark them.
"At this point the United Kingdom assumes its responsibility for the safeguarding of the shipwrecks", he said.
Toninelli said the rescue was coordinated by Libyan authorities and that the ship was in Maltese waters.
Its transport minister, Danilo Toninelli, wrote on Twitter: "The boat is now in Maltese waters and has a Gibraltar flag".
The Aquarius was sailing north in the Mediterranean Sunday in hopes of receiving docking permission from another country.
The group was picked up in the Mediterranean Sea by French humanitarian workers on Friday.
The vessel is reportedly now still at sea between Malta and Italy after MFS claimed both nations said they would not open their ports to the ship and those on board.
"Aquarius has now reached a standby position exactly between Malta and Italy and is awaiting further guidance", MSF said in a tweet.
A European Commission spokesperson said all diplomatic channels were being employed to find a country willing to take the migrants, . She added that while Britain could theoretically be considered as a destination port, it was not practically feasible to bring the ship there.
SOS Mediterranee said that "in a disturbing development, rescued people on board told our teams they encountered five different ships which did not offer them assistance before they were rescued by Aquarius". "The requests for the vessel to enter our ports are unwarranted and without legal standing", it said in a statement.
Italy's new populist government has vowed that no more private aid ships will bring migrants to Italian shores.
It ended up having to go to Spain with over 600 migrants it rescued transported with the help of an Italian escort.
Though departures from Libya have fallen dramatically this year, people smugglers are still pushing some boats out to sea and an estimated 720 people died in June and July when charity ships were mainly absent, Amnesty International estimates.
Protracted feuds between EU states over how to handle immigrants have thrown the issue back onto the European agenda.
European Union border agency Frontex said on Monday it counted 73 500 "irregular border crossings" into the bloc so far this year via the sea and the Western Balkans route, more than 40 per cent fewer than in the first seven months of 2017.
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