The gang also praised the Paris terrorist attacks, in which 130 people were killed on November 13th.
The four, all Kosovan citizens, were arrested as part of an anti-terror sweep conducted by police in Brescia in cooperation with Kosovan authorities, Corriere reported.
Described as "a highly dangerous group" with alleged links to jihadists in Syria, they are accused of “condoning terrorism” and “inciting racial hatred”.
Carmine Esposito, from Brescia's police unit, told Rai Tre on Tuesday that the group “threatened Pope Francis, celebrated the recent attacks in Paris and threatened the ex-US ambassador in Kosovo.”
In reference to Pope Francis, investigators found online threats made by the group, including one saying “this will be the last Pope”.
The arrests followed raids in the Italian cities Brescia, Vicenza and Perugia as well as Kosovo.
Police said "the [alleged] terrorist team propagated the ideology of jihad through social networks".
The gang's “mastermind” is believed to have lived in Italy before being arrested in Kosovo. The other three were arrested in Italy, where they have been living for some time.
Italy has upped its anti-terror crackdown since the Paris attacks on November 13th, expelling four Moroccans suspected of spreading extremist views a week later.
A manual containing details of how to carry out a terror attack was found on the computer of one of the four.
Italian police also last month announced a swoop on a European jihadist network that was allegedly planning to try to spring its leader out of detention in Norway.
Security has also been tightened at borders, airports and key sites across Italy.