Mr Salvini, who is also head of the hard right, anti-immigrant Lega party, could end up closing every Italian port.
Malta said the rescue operations took place in global waters off Libya and were coordinated by Italy.
"In the Mediterranean.there's Malta that does now welcome anyone, there is France that rejects [refugees] at its borders, there's Spain that defends its borders with the arms".
Tweeting on Sunday, Salvini said: "Starting today, Italy, too, begins to say NO to the trafficking of human beings, NO to the business of clandestine immigration".
Italy's hardline interior minister Matteo Salvini, in a joint statement with Danilo Toninelli, minister in charge of the Italian coastguard, insisted that Malta "cannot continue to look the other way when it comes to respecting precise worldwide conventions on the protection of human life".
Italy's new PM says to take 'moderate' line on tariffs at G7
This year, the summit will be Friday and Saturday in Quebec, Canada. "We're like the piggy bank that everybody is robbing". Trump has imposed tariffs on steel and aluminum imported to the United States from the EU, Canada and Mexico.
ROME-Italy's new populist government has denied permission to dock to an aid-group boat ferrying hundreds of migrants rescued off the coast of Libya, following through on a campaign pledge to halt mass migration to Italy and leaving the vessel stranded.
The League promisied voters during the Italian general election that it would take a tough stance on immigration. Italy is the entry point for migrants from North Africa going to Europe.
Salvini said he is considering action against organisations rescuing migrants at sea.
The mayors of Palermo, Taranto, Messina and Reggio Calabria, have also said they would be ready to welcome the vessel.
He said: "We have doctors on board who are taking care of them but it's not definitive care so they do need to be disembarked as soon as possible so they can get the best treatment that they can". "We need to have an idea of what port to go to, something that up to now we haven't had".
Migrants are rescued by staff members of the MV Aquarius, a search and rescue ship run in partnership between SOS Mediterranee and Medecins Sans Frontieres in the central Mediterranean Sea, June 9, 2018.
We have always welcomed rescue boats and vessels who saved lives at sea.
"It is our obligation to help avoid a humanitarian catastrophe and offer a safe port to these people, as such meeting with the obligations of International Law", said Sánchez in a press release made public on Monday.