He said Malta would be sending fresh supplies to the vessel.
"Our only objective is the disembarkation in a port of safety of the people that we rescued yesterday in hard conditions", it said, adding that it "took good note" of the Italian Interior Ministry's statements.
Salvini and Italian Transportation Minister Danilo Toninelli, who is part of the 5-Star Movement faction in the new government, said in a joint statement Sunday that it was Malta's responsibility to "open its ports for the hundreds of the rescued on the NGO ship Aquarius". "The people we saved were in a hard condition, at least 50 were at risk of drowning", he added.
The spokesman said it took place in the Libyan search and rescue area and was headed up by the rescue coordination centre in Rome, meaning Malta has no legal obligation to take in the migrants.
Italy's new interior minister has refused permission for a rescue vessel to drop off more than 600 migrants picked up off Libya's coast.
European charity SOS Mediterranee said on Twitter earlier on Sunday that its rescue boat Aquarius had taken on board 629 migrants, including 123 unaccompanied minors, 11 other children and seven pregnant women. Salvini campaigned on an anti-immigrant platform that also included a vow to expel hundreds of thousands of migrants already in Italy, even though experts doubt such mass deportations are feasible or financially viable. "Malta takes in nobody", he said. "France pushes people back at the border, Spain defends its frontier with weapons".
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Prime Minister Joseph Muscat has made it clear that Malta will offer to evacuate people who require urgent medical help, without prejudice to its stand in refusing entry to the ship. "The Good Lord put Malta closer than Sicily to Africa".
The standoff marked the first display of Italy's get-tough immigration policy under the right-wing, xenophobic League. He noted that other European countries are very much involved in current rescue operations in the Mediterranean - including a German aid group now off Libya - but no country is stepping up to actually take in the migrants.
Last week, Salvini said Rome should increase its deportations of migrants.
The charity added on Twitter: "We have acknowledged what was stated by the Italian interior minister to Italian media".
SOS Méditerranée spokesperson Mathilde Auvillain said the boat had received orders to head north after a series of sea rescues and was now was awaiting "definitive instructions". He has previously accused them of being in cahoots with human traffickers.