The men allegedly have contacts with Algeria's Salafist movement, which is believed to have links to al-Qaeda.
They were detained in Naples and Brescia, and were "potentially operative."
The Italian news agency Ansa named the suspects as Yamine Bouhrama, Khaled Serai and Mohamed Larbi, quoting Naples police.
In June Italy pounced on suspected Islamic extremists by arresting an Imam and five other men suspected of Salafist connections.
The Salafist Group for Preaching and Combat (GSPC) is the main armed Islamic organisation in Algeria.
It reportedly wants to topple the Algerian government, create an Islamic state and attack Western interests in the region.
Indonesian television has also aired a video tape naming Italy, along with the United States, Britain and Australia, as a terrorist targets for joining the US-led war on terrorism in Afghanistan and Iraq.
A man making the threats was identified by Indonesian police as Bali bombing suspect and fugitive, Noordin Top, Asia's most wanted terrorists.
Italy, which has a 3,000-strong military contingent in Iraq, has stepped up security following the 7 July London bombings.