The country is the last major state in western Europe not to legally recognize and protect homosexual couples, and Renzi had promised a law would be passed by the end of the year - a deadline now looking a bit tight.
While attempts by previous administrations to change the law have been thwarted by parties with deep ties to the powerful Catholic Church, this time the majority of opposition parties have said they support the bill.
But Renzi's coalition partner, the small New Centre Right (NCD) party, fiercely opposes parts of it.
The proposed law offers some of the benefits of marriage, such as being able to receive part of a deceased partner's pension, automatic inheritance and being able to adopt the child of a partner if it only has one legal parent.
In July, the European Court of Human Rights upheld discrimination complaints filed by three Italian couples, saying Rome should introduce some form of civil union - an embarrassing ruling which helped pro-civil unionists.
While 74 percent of Italians support the idea according to a recent poll, hundreds of thousands of people took to the streets of Rome in June to protest a change to the law.
A Senate vote on the bill is expected before the end of the year, after which it will move to the lower house of parliament.