Updated 8.50pm with Maltese government's reaction
Matteo Salvini has vowed Italy would bar a boat with some 450 migrants that he said was under Maltese responsibility.
Details on the boat are still sparse, but Italy's right wing deputy prime minister kept up his anti-migrant rhetoric and said his country cannot and would not let the boat dock.
The migrants' condition is not yet known.
A spokesman for the Maltese government said Malta was notified of a large fishing vessel with some 450 migrants on board as soon as the vessel transited from the Libyan search and rescue region to the Maltese search area.
When that information was relayed, the vessel was about 53 nautical miles away from Lampedusa and 110 nautical miles from Malta.
When contacted, the persons on board the vessel informed Malta that their intention was to proceed to Lampedusa.
"One has to stress that given that the vessel was on the high seas, Malta did not have the authority to give it instructions," the spokesman said.
Malta monitored the vessel to ensure it would give it immediate assistance should it have been required. By Friday night, the vessel was in Italian territorial waters.
"It is pertinent to note that Malta has satisfied all obligation under the applicable international conventions on coordination of search and rescue events," the government said.
The reaction was starkly different to that expressed by Mr Salvini through a social media post earlier: "The boat is in waters which fall under the jurisdiction of Malta, which has assumed responsibility for the rescue. Nothing happened for hours and the boat is now sailing towards Italy," Mr Salvini said in a social media post."
"As promised, I will not give up. Malta, the smugglers, and the do-gooders know this boat will not land here," he said.
Sappiano Malta, gli scafisti e i buonisti di tutta Italia e di tutto il mondo che questo barcone in un porto italiano NON PUÒ e NON DEVE arrivare.
— Matteo Salvini (@matteosalvinimi) July 13, 2018
Abbiamo già dato, ci siamo capiti????? pic.twitter.com/HmpA8x7rPY
According to Italian media reports, the Italian rescue authority alerted their Maltese counterparts about the whereabouts of the boat in Maltese search and rescue waters after 4am on Friday. An aircraft was sent to the area to confirm the location of the migrants, which includes minors.
"But it does not appear that Valletta has in the meantime sent its ships into the area, nor has it diverted merchant units capable of providing relief on the spot," a report in Corriere said. The port of disembarkation has to be Malta, the Italian government said.
Minutes later, Transport Minister Danilo Toninelli, also urged Malta to act.
"According to the maritime law, it's Malta that must send its own ships and open its own ports," he said on Twitter. "Our coast guard can act, if needed, in support, but Malta should immediately do its duty."
The large boats are particularly dangerous because they have often capsized in the past, trapping hundreds of people below deck as they sink.
This would be the second time in a month that Italy and Malta are openly heading for a dispute over who should assume responsibility for migrants rescued in the centre of the Mediterranean.
Last month, the MV Lifeline with 230 rescued migrants on board, were left stranded out at sea for almost a week after Italy refused to let the ship into its ports. It eventually docked in Malta, after nine countries had agreed to share the migrants in what was seen as an ad-hoc agreement.
Read: Lifeline migrants had been hoping to make it to Italy
Malta has since controversially barred NGO vessels from operating from its ports and charged the Lifeline ship captain with steering the ship within Maltese territorial waters without the necessary registration and licence.