Le Maire's remarks were "another unacceptable pitch invasion" Matteo Salvini, the leader of the right-wing League party which is in the process of forming a coalition with the Five Star Movement (M5S), declared in a tweet on Sunday.
"I didn't call for votes and confidence to continue on the road to poverty, precarity and immigration," he went on. "Italians first!"
And later he told reporters, "The French should attend to France and not interfere in other people's business" and challenged President Emmanuel Macron's government to discuss "migrants stopped at the [Franco-Italian] border".
The influx of migrants into Europe has seen immigration controls revived on borders where they had been abolished by the Schengen agreement, which came into effect in 1995.
Le Maire at the weekend predicted that the eurozone's financial stability would be put at risk if the new Italian government does not abide by previous government's commitments on "debt, the deficit and consolidation of the banks".
Contract for government
The League and M5S on Friday unveiled a "contract for government" that dropped an earlier pledge to leave the euro but opposes austerity and Brussels "diktats", as well as promising to clamp down in immigration.
M5S leader Luigi de Maio on Saturday said the government would be challenging France on another question - a controversial high-speed rail link between the central French city of Lyon and the northern Italian city of Turin.
The project "might have meant something 30 years ago but serves no purpose today", he said.
But Salvini does not agree with him and pointed out on Sunday that the two parties' agreement only committed them to "reexamine" the case.
De Maio and Salvini were to meet Italian President Sergio Mattarella on Monday afternoon to propose a name for the next prime minister.