"You don't negotiate when faced with violence," Nordio told a news conference.
Cospito, whose health is deteriorating after spending over 100 days on a hunger strike against the prison treatment usually reserved for mafia convicts, was moved on Monday to a Milan jail where medical facilities are better than the Sardinian one he has been in for the last few years.
But he is still being held under the 41 bis regime.
Nordio said a decision on whether he would stay on it would be made after the judicial authorities were consulted.
But the minister added that the fact the 55-year-old Informal Anarchists Federation (FAI) leader was on hunger strike would have no effect on the type of jail regime he is held under.
"The wave of acts of vandalism shows that the link between the inmate and his companions remains and that would tend to justify maintaining the 41 bis," Nordio said.
He added that the fact Cospito had been moved to Milan was purely linked to medical factors and was not sign that the State had "yielded".
Cospito, who has lost more than 40kg during his hunger strike and has lately taken to a wheelchair, slipped and fell in the shower and broke his nose last week.
He is serving 20 years for a bomb attack on a Carabinieri police training academy at Fossano near Cuneo in Piedmont in 2006 and a further 10 years and eight months for kneecapping Ansaldo Nucleare Managing Director Roberto Adinolfi in Genoa in 2012.
Italian diplomatic offices in Berlin and Barcelona were subjected to vandalism last week and anarchist groups were engaged in violent clashes with police in the Trastevere district of Rome on Saturday night.
A policeman was injured in those clashes and 41 people have been cited over them.
Anarchists are also thought to have been behind a Molotov cocktail attack on a Rome police station at the weekend, the torching of five cars belonging to telecoms giant TIM in the capital and of two local police cars in Milan.
These are only the latest in a series of such acts in Italy and abroad linked to anarchists in recent months.
Meanwhile Cospito's lawyer said on Tuesday the jailed anarchist leader now wants to stop taking food supplements.
"Today Alfredo Cospito was seen by a trial deputy I appointed, who found him worn out and learned that he had decided to stop the supplements," Flavio Rossi Albertini said during an interview on Rai Radio1 program, Menabò.
"This decision worries me, I hope to make him rethink."
Stopping vitamin and mineral supplements will further compromise Cospito's already precarious state of health.
ANSA
