The party launched its campaign on www.referendumroma2024.it, detailing actual costs incurred by the last 50 Olympics hosts and claiming it would cost Italian taxpayers "billions of euros".
It noted that Davos (Switzerland), Krakow (Poland), Oslo, Monaco and Hamburg (Germany) had all decided not to bid for 2024 following consultation with the public via debate or referendums, and said Rome should do the same.
"The candidature is official, it has the political and financial support of the government, you would think that everything's already been decided," said a statement by Radicali Italiani.
"But in fact, there is still time for public debate on the costs and benefits of a project that will cost us billions of euros in taxes."
Rome, Paris, Budapest and Los Angeles are all in the running to host the Games in 2024 although a number of other cities pulled out due to a lack of public support following referendums.
The Radicali Italiani party's secretary Riccardo Magi said "such an important decision for the future of the capital should be taken by the public."
"This is why we're asking Presidente (Matteo) Renzi to offer a referendum, as has been done in many other cities keen on becoming candidates."
The party notably underlined the spiralling costs of hosting the Games, claiming it cost London 2012 organizers £8.77 billion to host the Games in 2012 - over three times the estimated budget of £2.4 bn.
"Costs have always risen in respect to initial estimations, in some cases by 800%, with obvious consequences for the pockets of the citizens."
The host of the 2024 Olympics will be announced in September 2017.
Story continues below…