Were the draft to pass into law, people would be allowed to grow up to five cannabis plants for personal use and keep up to 15 grams of marijuana at home and five grams on their person.
It would still be illegal for people to buy or sell weed or smoke marijuana in public, but the Italian state could start issuing licenses allowing the drug to be grown and sold in a similar way to tobacco.
Several European countries, as well as a number of US states, have legalized marijuana in recent years, both for medical and recreational use.
Proponents of this approach argue that decades of international prohibition have manifestly failed to halt the worldwide spread of cannabis consumption.
In its latest annual report, Italy's Anti-Mafia Directorate criticized "the total failure of repressive action," to limit marijuana consumption.
The directorate said it supports relaxing existing laws in order to ease "the workload of the judiciary and free up resources for the security forces and judges in order to fight other crime".
While medical marijuana is legal in Italy, a string of other European nations including the Netherlands and Spain tolerate personal recreational use of the herb.
In the US, 23 states have legalized medical use, while four have decriminalized recreational consumption.
The draft was submitted for debate by foreign ministry undersecretary Benedetto Della Vedova, a libertarian who has also fought for gay rights, with the support of 200 MPs and senators.
But Italy is sharply divided on the matter, with Prime Minister Matteo Renzi's government on the fence.
Renzi said in May that the hot-button issue was "not on the agenda" for his team.
Catholic lawmakers have already made it clear they intend to fight the bill to the bitter end, including drowning the text with amendments.
With parliament recess about to begin, it will probably take MPs weeks to actually get to the core of the bill.
A coalition of centre-right Catholic lawmakers, "has presented 1,300 amendments to say no to the absurd draft", the group leader Maurizio Lupi said.
"We are completely opposed to the legislation, to the idea of sending out the message that it is alright to freely smoke a joint without a problem,"
Lupi said, adding that he was opposed to the bill both on health and public safety grounds.
Supporters of the bill say the criticism is baseless.
"The experience of states that have started legally regulating the marijuana market shows that the number of consumers has not increased, and that there has been no (negative) social or health impact," the draft text reads.
The only thing that does increase, the draft says, is tax returns.
According to Italian association Nativa, some three million kilos (6.6 million pounds) of cannabis are consumed in the Mediterranean country each year.