The Italian capital was vying with Paris, Los Angeles and Budapest to host the Games in eight years' time.
But a long and committed campaign by the Italian Olympic Committee came to a shuddering halt on Wednesday when mayor Virginia Raggi, who campaigned on an anti-Olympic Games ticket, insisted hosting the Games would be "irresponsible".
Prime Minister Renzi has been fully supportive of Rome's bid to host the Games for the first time since an iconic 1960 edition and, reacting quickly to Raggi's announcement on Wednesday, called it "sad and cynical".
But, asked on Thursday if the capital's bid was now a "closed chapter", the Italian premier told the 'La7 Otto e mezzo' programme: "I really think so, yes.
"It will depend on the formal decision to be made by the municipal council, but if the mayor's office are saying no, I would imagine the majority would vote with her."
And given Raggi's ruling Five Star anti-establishment party holds a resounding majority in the city council, after dominating the municipal elections with 67.15% of the votes, her decision is expected to prevail.
'A pretext to a building spree'
On Wednesday she claimed saying yes to the bid would be "irresponsible".
"We are effectively asking the people of Rome and of Italy to shoulder the debts. We just don't support it," said Rome mayor Raggi.
"Sport was an integral part of our electoral campaign, but we don't want it to be used as a pretext to a building spree around the city."
Raggi succeeded the controversial Ignazio Marino in October 2015 after promising to "fight corruption and bring back Rome's splendour".
A year earlier, a wide-reaching scandal had exposed the extent of criminal infiltration in a number of city bidding contracts, leading to Marino's downfall.
Calling the Games "a kind of dream that becomes a nightmare" for the city's inhabitants and above all "a great opportunity for the lobbyists", Raggi insisted: "We have far bigger ambitions for Rome."
She has pledged to undertake a vast revamp of the city's ailing and underused sporting infrastructure and claimed what most citizens really want is resolving "transport problems" and the "cleaning up of the city".
Renzi appeared to draw a line under Rome's 2024 bid when he added on the programme: "We're not going to organise Olympics against the wishes of an administration that would be hosting it.
"Raggi said that a referendum should be held, but she was the one who has said 'No'."
'Hearing 'no' hurts'
Italian Olympic Committee president Giovanni Malago has maintained a Rome Olympics would cost 5.3 billion euros and be financed exclusively from the Olympic Committee, sponsors and state funds.
He also claimed Raggi had crucially failed to understand the changes to the Olympic movement that would have helped Rome curb spending.
Host cities can now receive a 'significant financial contribution from the IOC', according to the International Olympic Committee, after it launched 'Olympic Agenda 2020' - described as a 'strategic roadmap for the Olympic movement'.
Rome 2024 campaigners will be hoping to keep their dream alive until October 7th, the deadline for candidates to submit the second installment of their bid dossier.
Speaking on Wednesday, Malago added: "Hearing 'no' hurts. I'm very sorry. It was possible to do this, and do it well.
"We will continue until I hear a formal no."