Thirteen sick migrants on Saturday left the Italian rescue ship docked for five days in a Sicilian port and Interior Minister Matteo Salvini said he was working on a "positive solution" for the remaining 137 people on board.
The migrants, mainly from Eritrea, have been stranded in the port of Catania since Monday because the Italian government is refusing to let them off the boat until other European Union states agree to take some of them in.
The United Nations called on Saturday for reason from all sides after a meeting of envoys from 10 EU states in Brussels a day earlier failed to break the deadlock.
"Frightened people who may be in need of international protection should not be caught in the maelstrom of politics," the UN refugee agency UNHCR said in a statement.
It appealed to EU member states to "urgently" offer relocation places to the rescued people, in line with an agreement at an EU summit in June, and in the meantime urged Italy to allow "the immediate disembarkation of those on board."
The only help from within the bloc came late on Saturday from Ireland whose foreign minister, Simon Coveney, said the government had agreed to accept 20 to 25 migrants.
"European solidarity is important and this is the right thing to do," the Irish minister said on Twitter.
Ireland's announcement followed an offer from non-EU member Albania to take in 20 of the migrants.
Italy's Foreign Ministry called Albania's offer "a signal of great solidarity and friendship which Italy greatly appreciates."
Salvini was in discussions with other non-EU countries who might be willing to follow Albania's example, an Interior Ministry source said earlier on Saturday.
Italy's anti-establishment government that took office three months ago has refused to back down, despite criticism from rights groups and the opposition.
The migrants that disembarked on Saturday — seven women and six men — were ordered off the boat by doctors after a check-up carried out at around midday.
They finally left the boat one-by-one some six hours later, stepping down a flight of steps to touch dry land for the first time since leaving Libya at least 10 days ago. They were taken by ambulance to Catania's Garibaldi hospital.
The doctors had recommended all 11 women on board be disembarked, but four refused to leave their partners on board.
Italian media reported that among the migrants who left the boat there were three cases of suspected tuberculosis and two of suspected pneumonia. Medical officials on the spot did not confirm this.
"Prospects of success"
More than 650,000 people have reached Italian shores since 2014 and Rome says it will not let any more rescue ships dock unless the migrants are shared out around the EU.
"I am totally untroubled and I am working, with good prospects of success, on a positive solution," said Salvini, leader of the right-wing League party, adding that he considered the criticism he received to be a "badge of honor."
Stefano Principato, a Red Cross representative, said the health of most of the migrants still on board "isn't particularly critical," adding their problems "are more psychological than physical."
Earlier this week Italy let 27 unaccompanied minors leave the vessel. Prior to that, 13 people needing urgent hospital attention were evacuated.
The mostly young men now on board shelter from the sun under a large green tarpaulin that covers around half the deck, with clothes attached to it hanging out to dry. Some occasionally wave to reporters gathered at the port.
Around 200 protesters gathered at the Catania port on Saturday, some waving flags of left-wing movements and parties, calling for the migrants to be allowed to disembark.
Meanwhile in Rome, Sicilian prosecutor Luigi Patronaggio questioned several Interior Ministry officials as part of a criminal investigation into "unknown persons" for holding the migrants on board the ship against their will.
Salvini has taken full responsibility for his ministry's actions and said any charges should be leveled against him personally, challenging the prosecutor to arrest him.
Separately, a group of charities appealed to a Catania administrative court on Saturday to order the migrants to be urgently disembarked.
The 5 Star Movement, the League's coalition partner, has so far backed Salvini's hard line, and its Transport Minister Danilo Toninelli, who is responsible for the country's ports, renewed the government's attacks on the EU.
"Nobody can give lessons to Italy on its humanitarian efforts," he said. "The government is only asking the EU give some sense to its own existence."