Italy became the first to announce a bid taking advantage of new International Olympic Committee rules allowing events to be staged in more than one city.
Speaking at the headquarters of the Italian Olympic Committee (CONI) during an end-of-year medals ceremony, Renzi said:"We are standing side by side with CONI because in September 2015, we will officially present our candidature to host the 2024 Olympic Games."
The prime minister said Rome would be the centrepiece of the Games bid but that "all the cities, from Florence and Naples to Sardinia" could be involved.
The Italian capital, which last held the summer Games in 1960, shelved plans to bid for the 2020 event two years ago due to concerns over rising costs as the country battled an economic crisis. Turin held the Winter Olympics in 2006.
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But with new rules passed by the IOC last week allowing countries to stage competitions across several cities, potential bidders are now able to spread the costs.
He added: "Rome will be the centrepiece of the project, then it will be up to CONI to decide which other cities will be involved."
Rome is the first city to officially announce it will bid for the 2024 Games, but the Eternal City can expect a tough competition.
The US Olympic Committee is to decide this week between Los Angeles, San Francisco, Boston or Washington for a probable American bid.