Most of them have been at sea for more than a week.
The Ocean Viking aid ship carrying 180 migrants is still waiting for authorisation to disembark in Italy.
Currently, it's anchored 4 kilometres off the Porto Empedocle town in Sicily.
The migrants were all given coronavirus tests and are waiting to be transferred to another ship, the Moby Zazà, where they'll be placed in quarantine.
They have been at sea for more than a week, after being rescued by the French NGO SOS Méditerranée between June 25 and 30.
There are 25 children and a pregnant woman among them.
The NGO said that "the unnecessary delay of this disembarkation has put lives at risk" and "tension" is escalating again onboard.
The Italian government sent a doctor onto the ship on Saturday after the NGO reported episodes of severe unrest, including suicide attempts and threats to the ship's crew, prompting demands for the immediate evacuation of 44 people due to "acute psychological distress".
The doctor excluded any mental condition, but acknowledged that the migrants were "tired, stressed and nervous". At the same time, he urged them to stop being "aggressive" in order to facilitate the disembarking operations.
"It only depends on you! Do not create a problem, do not fight, respect the crew, they saved you, and it will go quickly", he said, according to news agency AFP.
"We know that it is long, but the coronavirus slows things down in Italy so be patient, " he told the migrants, before being applauded as he left the ship.
"They believe him more because he represents Italy", Anne, doctor of the SOS Méditerranée, said, adding however that the situation needs to evolve quickly because "the 'placebo effect' will not last long".
"What is needed is to dock now," operations manager on board Nicholas Romaniuk stated, "and you have to do it before there is a death."
Operations impacted by COVID-19
"The acute psychological distress remains," Laurence Bondard, operations communications officer at SOS Méditerranée told Euronews from the ship as it was anchored off Porto Empedocle on Monday. "Many survivors have been expressing intent to harm themselves since several days now.
"They all have faced horrific past experiences in their countries of origin, in their journey in Libya, so SOS Méditerranée's medical team as well as our rescue team remain very vigilant and attentive this morning and throughout the day until disembarkation is actually over."
She explained that the COVID-19 pandemic had forced the NGO to operate in a very challenging context, with personal protective equipment limiting interactions and impairing communication with the migrants on board.
All survivors wear a mask and get their temperatures checked every morning and every evening, she said, while the NGO workers wear gowns, masks, protective eyeglasses, comply with social distancing rules and change their clothes before entering their cabins at night.
"All this did have an impact in our way of operating and also in the way we could interact with the survivors. They could never see our smiles and sometimes not even the eyes, hidden behind the eyeglasses," Bondard said.
"So we try and do our best to make our relationship with them as humane as possible, to humanise it in different ways. We have badges showing our pictures with our smiles, for example."
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