PALERMO, Italy (Reuters) - Italian police arrested six members of Sicily's Cosa Nostra mafia on Friday as part of an inquiry that uncovered a threat of violence against Interior Minister Angelino Alfano.

The arrests were made in a dawn raid in Corleone, one of the criminal group's strongholds. Police said the investigation had also helped them prevent a murder.

Telephone wiretaps recorded members of the gang talking about an attack on the Sicily-born minister, Palermo prosecutor Francesco Lo Voi told a news conference.

An investigative source told Reuters one suspect was recorded saying: "If it's all agreed, we'll hit him, right in the head."

Lo Voi said talking about an assassination attempt would be an exaggeration, partly because the mobsters had discussed striking when Alfano was completely unprotected by bodyguards, which was not likely to happen.

"You could say they were venting, but we need to grasp the significance of it," he said.

The wiretaps showed the grudge against Alfano stemmed from his readiness to toughen jail conditions for people convicted of mafia association, under the "41 bis" regime which suspends some of the usual rules on how to treat prisoners, subjecting them to near-total isolation.

The regime is a particularly touchy subject within the Cosa Nostra, or "Our Thing", which was Italy's most powerful mafia group in the 1980s and 1990s, but has been overtaken by the Calabrian 'Ndrangheta.

Former Corleone-based bosses Salvatore Riina and his successor Bernardo Provenzano have been arrested and imprisoned under the regime.

This investigation clearly showed that mafiosi still want revenge for the state's severe treatment, and people walking free are motivated by what goes on inside jails, Lo Voi said.

Asked by reporters in Brussels to comment on the matter, Alfano said: "We'll talk about that later."

At its most powerful, Cosa Nostra killed several public figures, including a Sicilian politician and brother of Italy's president, Piersanti Mattarella, as well as high-profile anti-mafia magistrates, Giovanni Falcone and Paolo Borsellino.

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No public figure has been murdered in recent years.

"The mafia has been significantly reduced but it still poses a threat to security and to the country that should not be underestimated," Justice Minister Andrea Orlando said.

(Reporting by Wladimiro Pantaleone, additional reporting and writing by Isla Binnie; Editing by Giselda Vagnoni and Dominic Evans)