Cospito has staged a hunger strike for 111 days and lost almost 50kg, spurring fears for his health.
Nordio said that Cospito, 55, whose protest has sparked attacks by anarchists in Italy and abroad, should stay under the 41 bis regime, normally reserved for mafia bosses, to stop him running activities from prison.
Nordio has judged that Cospito still constitutes a high social danger, sources said.
The minister rejected the request for revocation made by the prisoner's lawyer Flavio Rossi Albertini, who has now been informed of Nordio's decision.
The 41 bis had been ordered on May 4 last year by the then justice minister, Marta Cartabia, for four years.
Rossi Albertini said earlier on Thursday that Cospito is down from 120 kg to nearly 70 kg on his hunger strike and his health is concerning, particular after recently refusing supplements.
Justice Undersecretary Andrea Delmastro Delle Vedove said on Tuesday that it was the State's duty to ensure that Cospito gets the best possible medical treatment.
The 41 bis is normally reserved just for mafia bosses and Cospito is campaigning to get the regime lifted for all inmates, including mobsters.
Anarchists have staged protests and acts of vandalism in Italy and abroad in support of Cospito and there were big rallies in Rome and Milan at the weekend in which demonstrators clashed with police and some were arrested.
The case is also at the centre of a huge political row in which Delmastro is a lead player.
This row erupted when Giovanni Donzelli, Delmastro's flat mate and fellow lawmaker for Premier Giorgia Meloni's right-wing Brothers of Italy (FdI) party, revealed in the Lower House last week that Cospito had talked to mafia bosses about getting the 41 bis abolished and that four lawmakers for the centre-left Democratic Party (PD) had visited him in jail, where they also spoke briefly with mafia boss cellmates..
Delmastro was revealed to be the source of the information.
The PD has demanded Delmastro and Donzelli, a member of the Copasir parliamentary committee that oversees Italy's intelligence services, quit for, among other things, revealing allegedly secret information.
Justice Minister Nordio, however, has said that the information was sensitive but not classified.
Delmastro fuelled the row on Friday by saying that the PD lawmakers had given in to Cospito's demand that they meet other people being held under the 41 bis, including two mafia bosses, as a condition for the encounter with him.
"The PD will have to explain that bow to the mafiosi to the public," Delmastro said in an interview with local daily newspaper Il Biellese, which is based in his home town of Biella in Piedmont.
The PD has said it would take legal action against Delmastro and Donzelli.
Meloni has dismissed the Delmastro and Donzelli quit calls and defended her MPs while calling for everyone to "tone things down" in the row.
Judicial sources said on Tuesday that Cospito will be examined Saturday by a doctor named by his defence.
They also said that the head of the Italian penitentiary department, Giovanni Russo, was quizzed on Tuesday by Rome prosecutors along with two other officials in relation to a suit filed against Donzelli for his statements to the House.
ANSA