The move comes days after vandals trashed a staircase at the Palazzo della Civiltà Italiana, a building initiated by dictator Benito Mussolini and designed as a symbol of the Fascist era.
The building, in Rome's EUR district, opened its doors in 1953. It was renovated between 2003 and 2008, and has been home to the fashion house, Fendi, since last September.
Palazzo della Civiltà Italiana. Photo: Alberto Pizzoli/AFP
Franceschini said on Tuesday that a new bill, which sets a maximum prison terms of 15 years for those convicted of vandalizing Italy's monuments, is now ready.
The crackdown also comes almost a year after drunken Dutch football fans tore through the city, causing €5 million worth of damage, ahead of a game between Feyenoord and AS Roma.
Some €1.2 million worth of that damage was caused to the Barcaccia Fountain, at the foot of the Spanish Steps, and which had only just re-opened after a costly renovation.
The high profile story prompted former mayor Ignazio Marino to announce a clean-up of the city's fountains, while hiking fines for those caught throwing rubbish in them, or taking a dip.