“Italian authorities have informed us of their availability to disembark families on board: children, mothers, fathers,” Sea-Watch said on Twitter, two days after it rescued 65 migrants in distress off Libya.
Crew aboard the Dutch-flagged Sea-Watch 3 had warned the migrants needed medical and psychological care.
Seven children were disembarked, along with seven mothers, three fathers and an injured man, the interior ministry said.
Save the Children had appealed earlier Friday for an end to the odyssey of those who had risked the perilous crossing from North Africa to seek safety in Europe.
As the Italian coast guard began transferring the families to the island of Lampedusa, the charity insisted the remaining migrants should be allowed off too.
“All lives are equal, and have the right to a port of safety.
“If Italy's not willing to do so, the EU must shoulder its responsibilities and find a solution,” it said on Twitter.
On Wednesday, far-right Interior Minister Matteo Salvini had issued a snap directive banning the Sea Watch vessel from entering Italian territorial waters, saying “our ports are and remain closed” — a statement he repeated Friday.