MILAN — Spain will send a naval ship to Italian waters to pick up the 83 migrants who have been stranded in deteriorating conditions on a humanitarian group’s boat, the Spanish government said on Tuesday.

The office of the caretaker prime minister, Pedro Sánchez, a center-left Socialist, said a warship, Audaz, would depart from the southern Spanish port of Rota.

The vessel is expected to arrive at the Italian island of Lampedusa on Friday, the statement said, before then sailing to the main port on the island of Mallorca.

The announcement came as at least 15 migrants jumped into the sea from the rescue ship Open Arms, which is named for the organization that runs it, in desperate bids to reach the shores of the Italian island in the central Mediterranean after 19 days on the boat.