Salvini, also deputy prime minister, has been trying to take a hardline against migrants rescued at sea being brought to Italy, which he says bears an unfair share of their numbers.
The migrants were spotted aboard two makeshift boats, one by Tunisian fishermen and the other by Italians, on Wednesday, the day before at least 115 other migrants are believed to have drowned in a shipwreck off Libya.
The Italian coastguard sent a small boat to rescue those spotted by the Tunisians and took them to a larger coastguard vessel.
The Italian fishing boat stayed with the other vessel carrying around 50 migrants for 24 hours, 50 nautical miles from Malta and in its search and rescue area.
“We gave them water and crackers… we stayed in permanent contact with the (Italian) coastguard, but Malta never answered,” the fishing boat's captain, Carlo Giarratano, told journalists after arriving in western Sicily's Sciacca.
An Italian coastguard vessel eventually arrived to transport the migrants to the coastguard supply vessel, the Gregoretti.
“The government has officially asked the European Commission to coordinate operations to distribute the migrants who are currently on board,” interior ministry sources said.
“There are 135 people. Pending an official reply, no disembarkation port has been designated,” they said in a statement.
Nevertheless, on Wednesday police and the coastguard rescued 77 people, mostly women and children, three days after they left Libya and brought them all to Italy's Lampedusa.
Other migrant boats continue to arrive in Italy, including two from Tunisia with a total of 34 people on board that arrived in Lampedusa on Wednesday night.
Charity rescue boats, the main target of Salvini's ire, were not operating in the area at the time, with many of them detained pending prosecution of their crews.
German aid group Sea-Eye's vessel Alan Kurdi left Spain on Thursday headed for the waters off Libya.
French President Emmanuel Macron on Monday said 14 states had approved a plan to redistribute refugees rescued in the Mediterranean, and eight said they would actively take part.
A furious Salvini said at the time that the agreement underscored a demand that Italy “continue to be the refugee camp of Europe”.
The issue of what to do with the thousands of refugees still attempting to reach Europe by crossing the Mediterranean Sea has sparked a sharp response in some countries, with Italy saying it is bearing the brunt of the problem while its EU partners do little to help.
After snubbing Macron's meeting, Salvini said Italy “does not take orders and is not a partner: if Macron wants to discuss migrants, come to Rome”.
Last month, Italian authorities arrested the German captain of the Sea-Watch 3 charity boat, Carola Rackete, after she hit an Italian speedboat while docking without permission in Lampedusa.