The march was announced by the far-right Forza Nuova party for October 28th - exactly 95 years after Mussolini's own March on Rome, a mass demonstration which resulted in the National Fascist Party taking power in Italy.
Speaking in parliament on Wednesday, Minniti said the event "clearly recall[ed] the birth of the Fascist regime" and would "clearly contrast with the legal order".
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A group of 45 centre-left MPs wrote a letter to Minniti last week asking him to cancel the event after Forza Nuova appealed on social media for financial donations to fund the coaches, banners, and petrol necessary for the demonstration.
Rome authorities and police said at the time they had not received formal notice of the plans, and Minniti said this had still not been given.
"I can assure you that if formal notice of this event is given, authorities will make the necessary arrangements," he told parliament on Wednesday.
In response to the initial criticism, Forza Nuova's leader Roberto Fiore denied any "fascist or nostalgic" element to the march, and called it a "walk for security".
Officially, the so-called 'March of Patriots' had the aim of protesting "against an illegitimate government, to say definitively no to Ius Soli [a controversial proposal for a law which would give Italian-born children of migrants Italian citizenship if they fulfilled certain conditions], and to stop violence and rapes by the immigrants who have mobbed our country".
Italian MPs last week voted in favour of a law outlawing 'fascist propaganda', which included the sale and distribution of souvenirs or other products celebrating the regime. That proposal will now go to the Italian Senate in order to become law.