Mr Salvini rejected Paris’ apology for what it described as an honest “mistake,” prompting the French presidency to accuse him of deliberately “politicising” Friday’s incident.
An Elysée Palace spokesperson said: “We must put things into perspective. It was a mistake – the local prefecture admitted it had made a mistake.”
Italy asked France for “clarifications” after witnesses reported seeing a French police van cross the mountain border at Claviere, near the Italian ski resort of Sestriere, and officers making two men get out in a wooded area before driving back the short distance to France.
The men are suspected of being migrants of African origin.
A French official said the police officers behind the incident were new to the area, adding that their decision to cross the border into Italy without seeking prior permission had been an “error”.
Mr Salvini dismissed the French explanation, saying that “abandoning immigrants in an Italian forest cannot be considered a mistake or an incident”.
Mr Salvini said in a Facebook post: “What happened in Claviere represents an unprecedented offence against our country.
“We are facing an international disgrace, and [French President Emmanuel] Macron cannot pretend nothing has happened.
“I wonder if international organisations, starting with the United Nations and the European Union, do not find it vomit-making to leave people in an isolated area, without any assistance.”
He added: “Paris must inform us IMMEDIATELY of the identities of the immigrants left in the woods. Names, surnames, nationalities, dates of birth.”
Mr Salvini also posted a photo of the French president with a bright, red face and the text: “International shame. Italy won’t accept apologies.”
Meanwhile, Turin prosecutors said they were investigating another French foray to Claviere in August, when French border police officers allegedly checked up on two Italians living there.
The Italians were checked by four armed men in camouflage jackets who were “in all likelihood French,” Turin’s Chief Prosecutor, Armando Spataro, said.
The incident took place on August 2 and was reported on August 20, Mr Spataro added.
Tensions between the two neighbours have spiked as Rome has accused Paris of hypocrisy for refusing to take in its fair share of the hundreds of thousands of migrants who have reached Italy by boat since 2014.