One of the MPs has accused the opposition centre-left group of "bowing" to the mafia, while the PD, on the other hand, said it would sue the FdI lawmakers for defamation.
Cospito has been on hunger strike for more than 100 days to protest against the tough jail regime he is being held under, the 41 bis, which is usually reserved for mafia bosses.
His case has sparked a wave of violent protests, threats and vandalism by anarchist groups.
One of the FdI MPs, Giovanni Donzelli, who is a member of the Copasir parliamentary committee that oversees Italy's intelligence services, revealed in the Lower House last week that Cospito had talked to mafia bosses about getting the 41 bis abolished and that four PD lawmakers had visited him in jail.
Andrea Delmastro Delle Vedove, pictured top, the justice undersecretary with the portfolio for the penitentiary department, and Donzelli's flatmate, was the source of the information.
The PD is up in arms, demanding Delmastro and Donzelli quit for, among other reasons, revealing allegedly secret information.
Justice Minister Carlo Nordio, however, has said that the information was sensitive but not classified.
Italian left-leaning media have disputed Nordio's statement saying the wiretap was in fact a secret one that should have been kept under wraps.
Delmastro fuelled the row on Friday by claiming 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', based in his home town of Biella in Piedmont.
The PD said it would take legal action against Delmastro and Donzelli for damaging "the honour of the PD parliamentarians and offending the history of a party that has had, and continues to have, the fight against organised crime and any form of terrorism as its founding value".
The party said it hoped that Delmastro and Donzelli would not use their parliamentary immunity to dodge the case and called on Meloni to say whether she agreed with their attacks.
Cospito, meanwhile, has stressed to the people he has talked to in the Opera prison that he has nothing to do with the mafia, sources said on Friday.
He has said via his lawyer that he is staging the protest against the jail regime itself and not just to get himself out of it.
"I have nothing to do with the mafia," Cospito said, according to the sources.
"I want the 41 bis cancelled for everyone because it is an instrument that takes away fundamental freedoms.
"I have seen elderly and ill mafiosi (in 41 bis), people who are no longer dangerous".
Cospito, who has now lost more than 45 kgs during his hunger strike, said on Friday he would not be force fed if his conditions worsens to the extent he becomes unconscious, and also refused a psychiatric assessment.
He repeated that he has 'no intention' of interrupting his form of protest.
Prison doctors said they are worried, given his condition, about the possibility of the onset of heart disease.
Green-Left Alliance MP Ilaria Cucchi, who visited Cospito in jail on Friday, was extremelty concerned by his condition.
Cucchi's brother Stefano was a 31-year-old surveyor who was beaten to death while in Rome police custody in 2009.
"I found Alfredo Cospito's condition alarming to say the least and getting worse by the day and hour," she said.
"The thing that worries me most is that he has no intention of breaking his hunger strike, for him it is a political struggle".
In related news, Justice Undersecretary Andrea Ostellari was placed under a police escort Friday after threats from supporters of Cospito.
Ostellari, a Paduan lawyer and leading member of the rightwing League party, has been given the brief for inmates treatment as part of his work at the justice ministry, the Corriere del Veneto reported.
ANSA
