Police said that they believed the arrested people were setting up "Salafist jihadi" cells.
Poisons and ignition devices for explosives were seized during raids in the north Italian cities of Milan, Bergamo, Varese and Reggio Emilia as well as in Britain and France.
The suspects are also accused of falsifying identity documents allowing them to travel clandestinely from one European country to another.
The leaders of the group were named in the arrest warrants as Dridi Sabri, Mehidi Ben Nasr and Imed Ben Zarkaoui, all of whom operated out of Italy, according to the ANSA news agency.
"The cells were not planning attacks in Italy but were indoctrinating and recruiting people to send to places where terrorist attacks are an everyday activity," Giampaolo Ganzer, from the Milan anti-terrorism police, said.
He said the police investigation began in 2003 and that three suspects were still at large.
The men detained in Italy were expected to appear before magistrates later on Tuesday.
Meanwhile, French officials said a Tunisian suspect was arrested in a Paris suburb while the Portuguese news agency LUSA reported that another suspect was picked up in Portugal.
Separately, British police arrested two men after Italian police requested their extradition on terrorism charges.
Ali Ben Zidane Chehidi, 34, was arrested in Croydon, southeast England, and Mohamed Salah Ben Hamadi Khemiri, 53, was arrested in Manchester, northwest England.
"The two men were arrested on behalf of the Italian authorities under an extradition warrant in relation to allegations that between 2003 and 2005 they forged documents to facilitate the illegal entry into Italy of recruited volunteers to fight jihad in Iraq and Afghanistan," British police said in a statement.
A French police source told the Reuters news agency that the DST domestic intelligence service had been involved in a broader European operation linked to the arrests in Italy.
A number of suspects were detained but no further details were immediately available, the source said. The operation was ordered by prosecutors in Milan.