German interior minister Horst Seehofer welcomed the development in a statement, saying 94 of 123 migrants from ships that were allowed to land in Malta would be shared among European Union member states.
Migrants on a rescue boat that docked in the Italian island of Lampedusa against an explicit ban have disembarked after the vessel was impounded.
The migrants on board the Alex, run by the Mediterranea charity, have not yet disembarked in Lampedusa.
Italy's migration policy has led to clashes between NGOs and Italian authorities over rules that effectively close off the country's ports to their boats.
Salvini's refusal to open Italian ports to rescue boats has strained relationships with European partners and Malta, which along with Italy is the preferred destination for migrants trying to enter Europe by sea.
The Italian government had asked Mediterranea to head to Malta, but the NGO said the 11-hour journey would have been too long and risky.
Given the condition of those on board, the NGO had requested that the migrants, rescued from a rubber dinghy Thursday off Libya, be transferred to Italian or Maltese patrol boats.
Last month, Salvini issued a decree introducing fines of up to 50,000 euros ($57,000) for the captain, owner, and operator of vessels "entering Italian territorial waters without authorization".
Mediterranea thus follows the example of the captain of the Sea Watch 3 vessel, the German Carola Rackete, who entered the Lampedusa port last June 29 with 40 immigrants aboard after waiting for 17 days, for which she was sentenced to preventive house arrest and later freed by the justice system, much to Salvini's anger.
Sea-Eye said on its Facebook page that the crew of the Alan Kurdi brought the African migrants on board their vessel early Friday. On Sunday it was heading to Malta with 65 migrants on board but the Maltese government has not yet decided whether it will allow the vessel to dock there.
They applauded as the Alex docked on Saturday afternoon. "Human lives are not a bargaining chip" the charity tweeted on Sunday.
Migrants rest onboard of the NGO Sea-Eye's vessel "Alan Kurdi", July 7, 2019 in this image obtained by social media.
The Italian government has accused the NGO rescue boats of acting as a de-facto taxi service for migrants and of colluding with people-smugglers.
Despite Salvini's apparent firmness about closing Italian ports to migrants, dozens of migrants and asylum-seekers continue to arrive in Italy by other means, some rescued by Italian authorities.
Not only did the judge rule against the feelings of Prime Minister Salvini, this decision seemed to commend Ms. Rackete's actions, stating that she had fulfilled her duty to protect life.