Charities have branded the actions of the Italian government "illegal" after it prevented 250 people disembarking two migrant rescue ships.
There are 215 blocked on the Geo Barents and 35 on Humanity 1.
Children and people with medical issues were allowed to leave the ships in Catania, Sicily, but others were not. Two other rescue boats remain at sea.
The new Italian PM has promised to crack down on migrants travelling across the Mediterranean.
Italy is one of the main entry points into Europe and since the start of the year 85,000 migrants have arrived on boats, according to the UN.
Migrants set sail in small, overcrowded boats from North Africa - often they get into distress and are rescued by charity vessels.
In total 144 people were allowed to disembark the Humanity 1, which sails under a German flag, on Sunday morning. In the afternoon, 357 people were allowed off the Medecins sans Frontieres (MSF)-run Geo Barents, which sails under a Norwegian flag.
Italian Interior Minister Matteo Piantedosi said those who did not qualify as vulnerable would have to leave Italian waters and should be taken care of by the "flag state".
However, Humanity 1's captain is refusing to leave the port of Catania "until all survivors rescued from distress at sea have been disembarked", said SOS Humanity, the German charity that operates it.
In a series of tweets, SOS Humanity added that "the law of the sea obliges him [the captain] to bring all those rescued from distress to a safe place.
"Survivors have the right to an individual protection check, which can only be done on land. Rejecting the 35 people seeking protection aboard Humanity 1 from territorial waters is a form of collective refusal and is therefore illegal."
In tweets posted later on Sunday, SOS Humanity said it would launch legal action against the Italian government on Monday, claiming Italy's actions violate European law and the Geneva Refugee Convention.
It added it was unlawful to not let all the migrants disembark and it would also launch legal proceedings in Catania, to allow those who remained on board the vessel to disembark and begin asylum applications.
MSF, which runs the Geo Barents, also hit out at the Italian government's decision, saying it "is not considered legal under maritime law conventions".
The charity, known in English as Doctors Without Borders, added that "a rescue operation is considered complete only when all of the survivors have been disembarked in a safe place".
Both charities said everyone on board their ships was vulnerable as they had been rescued from the sea.
Two other boats run by non-governmental organisations remain at sea with no ports willing to accept them.
There are 93 people on the German-run Rise Above and 234 on the Ocean Viking, operated by the European charity SOS Mediterranee.
All four boats have reported people sleeping on floors and decks, the spread of fever-inducing infections and scabies, and food and medical supplies running low. Some migrants have been on the ships for more than two weeks.
Humanitarian groups and two Italian politicians have travelled to Sicily to protest against the process.
"Free all the people, free them,″ Italian lawmaker Aboubakar Soumahoro said, calling the government's new policy "inhuman".
Italy's new Prime Minister Giorgia Meloni put the issue of migration at the centre of her government in her maiden speech to MPs.
"We must stop illegal departures and human trafficking," she said, but stressed that she does not intend "to question the right of asylum for those fleeing wars and persecutions".
In a recent interview she also said responsibility for the migrants on board lies with the country where the ship is registered, otherwise it becomes a "pirate ship".
Credit: The BBC
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