Rome’s beleaguered mayor is facing calls to resign after allegedly putting pressure on the former chief of the city’s waste disposal firm to fudge the company’s accounts.

Virginia Raggi is accused of putting “undue pressure” on Lorenzo Bagnacani to manipulate the 2017 balance sheet of rubbish disposal firm AMA, with the objective of pushing the company into the red. Raggi sacked Bagnacani in February.

Raggi, who was elected in June 2016 with the Five Star Movement, the party governing nationally alongside the far-right League, allegedly suggested the balance sheet, which registered a profit of around €500,000 (£430,000), could be tweaked by withholding credits from cemetery services.

The motivation for the alleged request is unclear, although one theory is that Raggi wanted the company to be in the red so top managers would avoid getting bonuses. In an interview with La Stampa on Friday, Bagnacani also referred to a rule introduced by the previous mayor, Ignazio Marino, that foresees the company being privatised if it is in the red for two years running.

The allegations emerged via a recorded conversation between the pair that was published by the weekly magazine L’Espresso and in a complaint filed by Bagnacani to the police.

Raggi is persistently criticised for the increasingly shabby state of the Italian capital, which is blighted by potholes and where rubbish goes uncollected for days.

During the fiery exchange, which took place in November, she allegedly says to Bagnacani: “You have to give me a hand Lorenzo, you’re not helping me. The city is practically out of control, the unions are doing whatever the fuck they like.”

Bagnacani reportedly responds: “We must take into account that to give you a hand we can’t do what is not possible,” to which the mayor replies: “Get the auditors to say it. If you try to change your planned budget, try to make a draft to change your plan …You’re not giving me any fucking support, Lorenzo, what can I do?”

Rome city council eventually rejected the budget and Bagnacani and the rest of the AMA board were sacked for the company’s “failure to achieve its set targets”.

Raggi dismissed the claims as “much ado about nothing”. Writing on Facebook, she said: “They are talking about a stolen recording in which I say what I would have said to any other Rome citizens. I was hard with the ex-CEO of AMA because there is rubbish on the streets and I couldn’t accept that. There was no pressure, just a lot of anger towards those who didn’t do a good job of what they were paid to do.” She added: “They continue to throw mud at me but I have strong shoulders and will continue to defend my city and citizens.”

The council said in a statement on Thursday that there was no pressure put on the former CEO other than “the simple application of norms”. “The balance sheet proposed by Bagnacani broke the norms and would have guaranteed bonuses for the CEO and the managers,” the statement added.

Raggi is not under formal investigation but is being urged to resign if the recording is legitimate.

“If true, it would be the confession of a serious crime and a clear admission of her incapacity to govern,” said Erika Stefani, the League’s minister for regional affairs. “As per the rules of her Five Star Movement party, we expect her immediate resignation.”

Matteo Salvini, the deputy prime minister and leader of the League, said: “If she says the city is out of control, I say: change jobs.”

Salvini consistently chides Raggi, who was cleared of cronyism and abuse of office allegations in October, over the state of Rome as he strives to build support for the League in the city ahead of mayoral elections in May 2020.

But his own party is mired in controversy after Armando Siri, the League’s deputy transport minister, was placed under investigation this week for alleged corruption. Danilo Toninelli, M5S’s transport minister, stripped him of his duties pending further clarification in the investigation.