"If an official apology doesn't arrive, prime minister Conte would be right not to go to France," Salvini told reporters after demanding that France take in more migrants.
Macron had blasted Italy for its "cynicism and irresponsibility" in refusing to welcome 629 migrants left stranded on a French charity's rescue ship in the Mediterranean before Spain agreed to take them in.
Gabriel Attal, the spokesman for Macron's party, called Italy's actions "nauseating".
Italy's Foreign Affairs Minister Enzo Moavero Milanesi summoned the French ambassador to Rome over the comments on Wednesday, saying in a statement that "the Italian government considers unacceptable the words publicly pronounced yesterday in Paris".
Milanesi added that the comments made by France were "compromising relations between Italy and France".
France's foreign ministry responded by saying that it is "perfectly aware" of the pressure on Italy as it copes with an influx of migrants from Africa, adding it is "committed to cooperation and dialogue" with Rome.
Salvini's far-right League party campaigned on taking a hard line on migrants ahead of March's election and rose to power as part Italy's eurosceptic, populist government that took office this month.
Also on Wednesday, Austrian Chancellor Sebastian Kurz said that the hardline interior ministers of Austria, Germany and Italy have formed an "axis of the willing" to combat illegal immigration into the EU.
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