A series of raids across the country was targeting 18 people, they said. Some had been arrested in Italy, including the group's suspected spiritual leader, but others were believed to have left the country.
"We don't have proof, we have strong suspicion," said Mario Carta, head of the police unit leading the investigation said when asked for more details on a possible attack against the seat of the Catholic Church.
He said that, in intercepted telephone calls, investigators had heard the suspects say they would launch a "big jihad in Italy," conversations that also suggested a target might be the Vatican.
The group had "an abundant amount of weapons and numerous faithful willing to carry out acts of terrorism in Pakistan and Afghanistan before returning to Italy," police said in one of a series of statements.
All the suspects are Pakistanis or Afghans, Mr Carta said, adding that the operation was still in progress.
European governments are increasingly worried about the threat of "sleeper" militants apparently living normal lives in their countries but who are then activated to stage attacks at home or abroad.
Police wiretaps had determined that two people among the 18 targeted by arrest warrants were suspected of being part of a group that had protected al-Qaeda leader Osama bin Laden, who was killed by US special forces at his hideout in Abbottabad, Pakistan in 2011, a statement said.
The investigation, carried out by Italy's anti-terrorism DIGOS police branch, led to the arrest of an Imam in the northern city of Bergamo. He was suspected of being the spiritual leader of the group and had collected funds purportedly for religious purposes from Pakistanis and Afghans in Italy, police said.
The group supported the "armed struggle against the West", and wanted to incite a popular uprising against the Pakistani government so it would stop its backing of US forces in Afghanistan.
The United States has withdrawn most of its forces from Afghanistan. However, a relatively small number remains for training and special operations, while Washington is also carrying out drone strikes on Taliban militants.
The money was sent to Pakistan by members of the group who managed to avoid Italy's currency control regulations. In one case, 55,268 euros ($60,160) were carried to Pakistan on a flight from Rome to Islamabad.
But police said much of the money was moved through the trust-based transfer system known as hawala, which predates the time of the Prophet Mohammed, and which is the banking system of choice in Afghanistan's cash-based economy.
Some of those under investigation were believed to be involved in attacks in Pakistan, including one that killed more than 100 people in a market in the northwestern frontier city of Peshawar in 2009, the police added.
Most of the warrants centred on the Italian island of Sardinia, but the operation covered a total of seven Italian provinces, the statement said.
The organisation arranged for Pakistanis and Afghans to get into Italy under work contracts or as refugees seeking asylum and later sent some to cities in northern Europe, police said.