Seventeen people were targeted in the raids across Europe - 16 Kurds and a Kosovan. Six of them have been arrested in Italy, four in Britain and three in Norway.
Several members of the group have travelled to Iraq and Syria to fight for the Islamic State group, police said.
Investigators said the network was trying to free Norway-based fundamentalist preacher Najmuddin Ahmad Faraj - also known as Mullah Kreka - who is listed as a terrorist by the United States and United Nations.
Giovanni Governale of the Italian police's Special Operations Group told journalists the operation had "dismantled an integrated cell that included - in addition to Italy - Britain, Norway, Finland, Switzerland and Germany".
The network developed "on the 'dark web', little-known (Internet) platforms that we have managed to penetrate," Governale said, adding that the swoop has allowed police to scupper "a process of recruitment, of sending (fighters) into combat abroad".
Governale said the network "was about to continue sending many other jihadists abroad; it was about to carry out attacks, including suicide bombings, to try to free their chief, Mullah Krekar".
The 59-year-old, a Kurdish Iraqi, has been living in Norway since 1991.
He has been at risk of deportation since 2003 after Norwegian authorities ordered him to be expelled as a threat to national security.
While courts have upheld the ruling, Norwegian law bars him from being deported to Iraq, where he risks the death penalty.
Krekar also founded the radical Islamist group Ansar al-Islam, but insists he has not led it since 2002.
Among those arrested in Italy was Abdul Rahman Nauroz, who police said was “particularly active in recruitment activities” with his apartment in the northern city of Merano being used as a “place for secret meetings and a crossroads for aspiring jihadists”.