Italy’s far-right interior minister, Matteo Salvini, has reluctantly authorised 27 migrant children rescued at sea to disembark from a charity vessel anchored in limbo off Lampedusa island for days.

In a letter on Saturday, Salvini told the prime minister, Giuseppe Conte, he could authorise the “alleged” minors to leave the Open Arms ship, despite it being “divergent to my orientation.”

However, the remaining 105 adults and two accompanied children must stay on board in what the charity Proactiva Open Arms said were “untenable” conditions.

“The go-ahead for the disembarkation of these people is the exclusive responsibility of the prime minister,” Salvini wrote in reply to a humanitarian request from Conte. The interior minister has the final say on border issues.

The charity said it would need time to break the news to the migrants that most of them must remain on board. Some were rescued more than two weeks ago.

“They will be evacuated by the coastguard of Lampedusa,” it tweeted.

There have been many standoffs between a charity vessels rescuing migrants making the perilous journey across the Mediterranean and Salvini, but this one is set against the background of a political crisis in Rome that is threatening to upend the government.

Salvini, who is also deputy prime minister, has gained popularity through his hardline policies against migrants and asylum seekers. He agreed last year with coalition partner the Five Star Movement’s (M5S) Luigi Di Maio for Conte to be prime minister.

But the men’s relationship has unravelled since Salvini, leader of the anti-migrant League, last week pulled his party out of the ruling coalition in the hope of toppling the 14-month-old government.

The migrant standoff has taken centre stage in the political crisis, pending a potential Senate no-confidence vote in Conte on Tuesday.

The ship has been anchored within swimming distance of southern island Lampedusa with 134 migrants on board since Thursday.

A Sicily prosecutor on Saturday sent judicial police to coastguard headquarters in Rome as part of a probe into alleged kidnapping and abuse of office because the Open Arms has not been allowed to dock.

Police took records of communications between the interior ministry and rescue services in order to verify the chain of command for who is preventing the ship from docking, the left-leaning Repubblica daily said.