The agency said without quoting sources that the alert was issued at a summit meeting of police and intelligence chiefs at the Interior Ministry on Wednesday night.
The Pope - whose visit last weekend to the Bosnian capital Sarajevo was preceded by the discovery of land mines along the route of his motorcade - and international airports in Italy were among potential targets, the agency said.
It said the report sounding the alarm had been drawn up by the Italian military intelligence agency, Sismi, and referred to the crisis in Europe's relations with Iran as the possible spark for attacks by Islamic militants.
The Interior Ministry declined to comment specifically, but said in a statement: "Vigilance in the face of all possible terrorist threats is permanent and systematic." Citing the need for "maximum reserve", it added: "Indiscretions and alarmism can only harm the cause of public security."
The Vatican initially also declined to comment, but its Secretary of State, Cardinal Angelo Sodano, later told Italian television that the Pope was not "particularly alarmed".
He went on: "These [news] reports have also reached us but the attitude of me and my colleagues and above all of the Holy Father is as it always was. We all trust in the Italian authorities ... and we all pray for the Holy Father that Divine Providence will protect and safeguard him as it has throughout all these years."
Wednesday's alert follows a finding by a German court that the Iranian leadership had ordered the 1992 killing of four Kurdish opposition activists in Berlin.
In the aftermath of the court case, all European Union countries, except Greece, recalled their ambassadors from Iran for consultations.
The verdict prompted an official protest from Iran and unleashed a wave of demonstrations in Tehran where thousands of people took to the streets.Reuse content