Salvini, head of the far-right League, is suspected of sequestration and abuse of power for having refused to allow around 100 migrants to land in Italy in August 2019.
He had blocked a ship, the Open Arms, from docking in a port, forcing it to anchor off the island of Lampedusa while conditions on board deteriorated.
The migrants that had been picked up at sea were finally able to disembark on the orders of a local prosecutor.
On Saturday, the judge postponed proceedings until March 20, at which point the former minister is to find out if he will face charges or not.
“I am totally at ease and proud of what I did,” Salvini told media following the closed-door hearing. “I am sorry only for the cost of the procedure that is being borne by Italian taxpayers and the magistrate's time that I have wasted.”
Open Arms said in a statement that the case was also directed at the Italian and European Union governments, which it said had violated international conventions on sea rescues and refugees rights.
Salvini was forced out of his position as interior minister shortly after the affair owing to a government crisis he himself had provoked.
Since then, the coronavirus epidemic and dire economic conditions stemming from it have replaced immigration as the main concerns of most Italians.
Restrictions stemming from the pandemic also resulted in a sharp decline in the number of illegal immigrants who entered Italy last year.