"No citizen is above the law," Mattarella told lawmakers and dignitaries at the lower house of parliament, stressing that there was no special privilege for anyone – "neither those in public office, nor politicians".
While he didn't mention Salvini by name, many people took his comments to be a jab at the interior minister, who is facing charges of illegal confinement after he refused to allow more than 100 people rescued at sea to get off an Italian coastguard ship, the Diciotti, that arrived in Sicily last month. After several days in port the vessel was eventually allowed to disembark when the Catholic Church brokered a three-way deal with Ireland and Albania to take the migrants in.
Public prosecutors in Sicily are currently investigating whether there is enough evidence to pursue the case.
Salvini, who has dismissed the accusations against him, showed himself defiant once again after the president's remarks.
"President Mattarella pointed out today that 'no one is above the law'. He's right," the interior minister and deputy prime minister wrote on Facebook. "That's why I, respecting the law, the constitution and my commitment to the Italian people, have closed and will close the ports to human traffickers.
"Investigate me and put me on trial, I'll keep going."
READ MORE: Italy's Salvini faces probe into treatment of stranded migrants
President Sergio Mattarella (centre) swears in Interior Minister Matteo Salvini (left). Photo: Francesco Ammendola/Italian Presidency/AFP
Mattarella was speaking at a memorial for former president Oscar Luigi Scalfaro, who headed the Italian state throughout the far-reaching political corruption scandals of the 1990s that saw scores of lawmakers disgraced and several parties disbanded.
Quoting his predecessor, Mattarella said that "justice can never be right-wing, centre or left-wing... The Italian Republic and its democracy are governed by rules. Respecting them is indispensable: always, no matter the intention of those who propose breaking them."
The president has clashed with Salvini before, in the heat of post-election negotiations when he vetoed the anti-euro finance minister nominated by a coalition of Salvini's League and Italy's largest party, the Five Star Movement, and moved to appoint a cabinet of technocrats instead.
After several days of uncertainty and amid threats to start impeachment proceedings, the coalition eventually agreed to appoint a different finance minister and switch their nominee to a less sensitive portfolio.
Since the coalition government took office in June, Mattarella has also criticized Salvini's hardline policies on migration, saying that talk of closing borders was a knee-jerk response and calling for a more rational solution.