Three migrants who suffered "medical complications which require specialized care" and an escort were brought to the southern Italian island of Lampedusa late on Thursday, Spanish charity Proactiva Open Arms said on Twitter.
"All of the people on board need to disembark urgently. For humanity," Proactiva Open Arms added, Presstv Reported.
This is the umpteenth standoff between a charity vessel rescuing migrants making the perilous journey across the Mediterranean and Italy's far-right Interior Minister Matteo Salvini, but this time set against the background of a political crisis in Rome.
Thursday saw sparring between Prime Minister Giuseppe Conte and Salvini, who last week pulled his party's support from the ruling coalition in the hope of toppling the 14-month-old government.
Salvini's anti-immigrant League party has been squabbling with coalition partner the anti-establishment Five Star Movement (M5S) over a host of issues.
"France, Germany, Romania, Portugal, Spain and Luxembourg have told me that they are ready to welcome the migrants," Conte said in an open letter to Salvini, who has sought to bar all charity rescue vessels from entering Italian waters.
In a distinct change of tone since the coalition disintegrated last week, Conte slammed what he called Salvini's "obsessive focus" on an immigration policy reduced to the phrase "closed ports".
Salvini has taken a hard line against migrants rescued at sea being brought to Italy, which he says bears an unfair burden as the first port of call for refugees from several countries.
Responding to Conte, Salvini wrote on Facebook: "It is clear that without (my) resolve, the European Union would never have lifted a finger, leaving Italy and the Italians on their own like (previous governments) did for years."
'Listening to my conscience'
After Salvini pulled the plug on his coalition with M5S last week, he had hoped for a no-confidence vote but his gambit failed.
His abandoned M5S partner found an unexpected ally in the opposition Democratic Party (PD) and they defeated Salvini's bid for a swift vote to bring down the government in which he is also deputy prime minister.
The fate of the migrants aboard the Open Arms vessel, operated by Spanish charity Proactiva, found itself at the centre of the political crisis in Rome.
Earlier this month, Salvini signed a decree banning the Open Arms from Italian waters, saying it was to protect public order.
But Proactiva appealed to an administrative court which on Wednesday suspended the decree.
Salvini then signed a new one blocking the ship, but in a demonstration of his diminished power, Italy's defence minister blocked it on Thursday.
Elisabetta Trenta, an M5S party member with the authority to sign off on Salvini's decree, announced that she has decided not to do so after "listening to my conscience".
It is estimated Salvini enjoys up to 38% support among the electorate, thanks largely to his hard-line against immigrants.
The mainly African migrants aboard Open Arms had been plucked from boats in the Mediterranean this month with weather conditions encouraging more departures from Libya.
Both Italy and Malta have refused the boat permission to dock and disembark its passengers.
Five migrants disembarked at Lampedusa on Thursday "for psychological reasons", the NGO said.
Another rescue ship, the Ocean Viking, operated by SOS Mediterranee and Doctors without Borders (MSF), is also looking for a port to dock with more than 350 migrants on board.