First reported by Italian daily La Repubblica on Saturday, the scandal has caused widespread outrage across the nation.
It involves five unnamed MPs who are accused of applying for the monthly €600 payment.
News reports said the MPs in question came from the opposition right-wing League party, the ruling populist Five Star Movement (M5S) and the centrist Italia Viva party.
Not all the MPs who applied for the bonus received it, La Repubblica subsequently reported on Monday, with sources saying only three had actually got the pay-out.
Another 2000 elected officials on regional and city councils also claimed the aid, according to the initial report.
The government aid of €600 for the months of March and April and €1000 for the month of May was intended to support self-employed and seasonal workers affected by the coronavirus lockdown.
Some €6.9 billion in payments were distributed to Italians.
To qualify, applicants needed to have to have a VAT number – which includes the self-employed and other categories of independent workers, including freelance journalists – and to be able to demonstrate that the crisis had wiped out at least two-thirds of their usual income.
The deputies were able to claim the benefit because they too have VAT numbers, so technically they have not done anything illegal.
But after being caught by a government anti-fraud body, they were slammed by fellow politicians for going against the “spirit of legislation”.
Leaders of all parties have called for the identities of the parliamentarians, who are protected by a privacy law, to be made public and for them to resign.
“It’s shameful, really indecent,” Foreign Minister Luigi Di Maio of the M5S wrote on Facebook, calling for the money to be returned and the lawmakers to step down.
“These people no longer have the right to hold public office.
“They have gone against the country during the most difficult period.
“They have soiled Italy’s name around the world … they cannot and must not get away with it.”
League leader Matteo Salvini initially said the alleged should resign, but later called for their suspension.
The Italia Viva party, founded by former prime minister Matteo Renzi, denied that any of its parliamentarians had received the bonus.
A number of local councillors came forward to say that they too had claimed the bonus or other government support during the crisis, defending themselves on the grounds that politics wasn’t their only job.
Anita Pirovano, a Milan councillor and member of the left-wing Left Ecology Freedom party, on Monday admitted she had received the benefit.
“I’m a psychologist, I have a mortgage, I do the shopping, I provide for my daughter and occasionally I like to go out and go on holiday,” she said.
“I wouldn’t be able to make a living as a politician.”
Those accused reportedly earn a salary of €13,000 a month as politicians.
The scandal is particularly jarring for ordinary Italians, thousands of whom have not received the payments they are entitled to through the government scheme.
With ANSA