Scrapping the small change would amount to savings of €20,000 each year, said the party's Head of Innovation Sergio Boccadutri, who proposed the measure as a budgetary amendment.
According to the MP, each one-cent coin costs 4.2 cents to manufacture, while a two-cent coin costs 5.2 cents.
Since the introduction of the euro in Italy, the mint has spent billions on creating the small denominations, which are rarely accepted in parking meters, toll booths, or vending machines - meaning they often end up forgotten in drawers or old coat pockets.
Across the eurozone, four countries have already largely stopped the production of the two lowest-value coins.
In Belgium, Finland, Ireland and the Netherlands, prices are often rounded to the nearest five cents when consumers pay with cash, though the small coins remain legal tender.
Boccadutri previously suggested introducing rounding in Italy in 2014, when he was an MP for the now-defunct Left Ecology Freedom party.
The Chamber of Deputies, the lower house of Italy's parliament, voted almost unanimously in favour of the proposal, committing the country to "examine the possibility of introducing measures to reduce significantly the demand for one- and two-cent coins".