A migrant rescue ship carrying more than 80 people was evacuated near Italy's southernmost island on Tuesday, ending a 19-day standoff that pushed 15 passengers to jump into the sea to escape deteriorating conditions aboard.

Sicilian prosecutor Luigi Patronaggio ordered the seizure and immediate evacuation of the ship off the island of Lampedusa. The prosecutor boarded the vessel and met with port authorities, amid an investigation into possible kidnapping charges resulting from the refusal of hard-line Interior Minister Matteo Salvini to allow the migrants to disembark, the news agency ANSA reported.

The passengers had been on the Spanish-flagged ship Open Arms since they were plucked from the Mediterranean nearly three weeks ago.

Migrants on the Open Arms rescue ship preparing to disembark on the Sicilian island of Lampedusa on Tuesday. (AP)

Salvini had refused to open Italian ports to the vessel even after six countries stepped forward to take the migrants.

The group stepped ashore about an hour after the resignation of Italian premier Giuseppe Conte, who accused Salvini of sacrificing the country's 14-month-old populist government out of eagerness to take the top job himself.

The captain of the Open Arms had previously told Italian officials the crew of 17 was no longer able to maintain control and described the situation as "desperate." After one Syrian national jumped and was rescued and brought to shore on Lampedusa, two more groups followed his lead. A ferry crew took them to land, sparing them a return to the ship.

Dozens of others have been evacuated in recent days for medical reasons or because they're minors. Officials said tensions on board were running high, with fights breaking out among the migrants.

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The temporary confiscation of the rescue ship by the prosecutor "is a cost that Open Arms assumes to secure that the people on board can be assisted," said the Spanish NGO's founder, Oscar Camps, on Twitter.

"We consider indispensable prioritizing their health and security in this humanitarian emergency," he wrote.

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Spain said it would take three days for its navy ship, the Audaz, to reach Lampedusa from the Spanish port of Rota, and it wasn't immediately clear how long it would take to escort the Open Arms to the Spanish island of Mallorca.

Emilio Damiá Marqués, the commander of the Audaz, told Spanish public broadcaster TVE from Rota that his ship, carrying 62 people including a doctor, was expected to arrive at the Italian island by Friday afternoon.

The Associated Press contributed to this report.