"It can go where it wants, not in Italy!" far-right Interior Minister Matteo Salvini said on Twitter on Monday, mentioning France, Germany, Britain or Malta as possible destinations. "No more to human trafficking and their accomplices", he said.
Doctors Without Borders said European governments tend to focus their efforts on "propping up the Libyan JRCC (joint rescue co-operation centre)", but that the two rescues on Friday underlined the unreliability of the system.
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".
Italy's transport minister has called on the United Kingdom to take responsibility for 141 people rescued by a ship sailing under the flag of the British territory of Gibraltar.
They boarded their boat, the Aquarius, and tried to dock in Italy.
Malta said on Saturday it would not welcome the ship either.
Danilo Toninelli, the transport and infrastructure minister and a senior member of the anti-establishment 5-Star Movement (M5S), said via Twitter on Monday that the rescue was co-ordinated by the Libyan coast guard and the rescue ship was in Maltese waters, sailing under the flag of Gibraltar.
The rubber dinghy was taking in water when it was found, however, all migrants were rescued by an AFM patrol vessel.
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The rescue came as a new migrant dispute was developing, with the migrant rescue vessel Aquarius saying that both Malta and Italy had refused to allow it into their ports. "The requests for such vessel to enter ports are unwarranted and without legal standing", the government statement said.
According to the statement, Aquarius was made off the Libyan coast, Tunisia and Italy (Lampedusa) in an operation which was coordinated by the Libyan authorities.
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.
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.
For years, Italy pleaded with its European Union partners for help with a massive influx of arrivals from Africa that has seen 700,000 people cross the Mediterranean and land in the country since 2013.
Doctors Without Borders said numerous people who were rescued are weak and malnourished.