One of the smugglers' boats, a small wooden craft with 25 migrants, appears to have been at sea for almost 35 hours, the groups said.
Italian transport minister Danilo Toninelli claimed the United Kingdom is responsible for the migrants on board as the rescue ship that picked them up is sailing under the flag of the British territory.
On Friday the group's chartered ship Aquarius, which it operates in partnership with Doctors Without Borders, rescued 141 people in waters off Libya.
In June, the vessel was at the centre of standoff between Italy and Malta and remained stranded at sea for days, with more than 600 migrants on board.
In a statement, the Armed Forces of Malta said the rubber dinghy was spotted during a routine border patrol.
The director of the French port of Sete on the Mediterranean coast said meanwhile yesterday that he would be prepared to let the boat, carrying migrants mostly from Somalia and Eritrea to dock if the government gave the all clear. "We're asking them to be responsible and find a safe port in the Mediterranean", she said, accusing Italy and Malta of flouting worldwide maritime law.
Matteo Salvini, the country's far-right populist interior minister, also wrote: "It can go anywhere it wants, NOT in Italy".
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"Malta was neither the coordinating nor the competent authority. and therefore has no legal obligation to make the arrangements to provide for a place of safety".
She added that Libya's maritime authorities, who coordinated the rescue, said: "They could not offer us a safe port and that we had to contact other rescue coordination centers".
Due to pressure from Italy and Malta, most charity ships are no longer patrolling off the coast of Libya.
The Maltese authorities said they were monitoring the situation and in touch with overseas counterparts.
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 percent fewer than in the first seven months of 2017.
Migrants are seen resting on board the MV Aquarius rescue ship run by SOS Mediterranee organisation and Doctors Without Borders during a search and rescue (SAR) operation in the Mediterranean Sea, off the Libyan Coast, August 12, 2018. The migrants will be brought to Malta in the afternoon, sources said.
"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", the group quoted Nick Romaniuk, its search and rescue coordinator as saying.