Democratic Party commissioner in Rome, Matteo Orfini, and Paolo Centro, the secretary of Left, Ecology and Freedom (SEL) said that if Marino didn't step down before 4pm then they would call for a no-confidence motion against him in city hall, Ansa reported.
The threat came as Rome's deputy mayor, Marco Causi, and executive transport councillor, Stefano Esposito, resigned. Esposito said the situation would “inevitably lead to the end of this administration”.
But Ignazio, who took office in June 2013, has so far resisted calls to step down.
In a statement on his Facebook page, Ignazio Marino insisted all the money had been spent legitimately on official entertainment but that he would cover the cost as a personal gift to Italy's financially-strapped capital.
"With this gesture I want to draw a line under the pointless and surreal polemics of recent days, which do Rome no good," the centre-left mayor wrote.
That appeared a forlorn hope.
The story dominated media headlines on Thursday, with newspapers publishing evidence suggesting that at least a handful of the paid-for dinners had been attended only by Marino and his wife.
Marino's administration has been buffeted by a seemingly never-ending string of damaging stories since he was elected in 2013 for a five-year term.
These range from the revelation that he drove his Fiat Panda in traffic-restricted areas of the city with an expired permit to stories that regularly suggest Prime Minister Matteo Renzi regards his Democratic Party colleague as a liability.
Suspected smear campaign
Marino copped the blame when a notorious mafia figure who styled himself the 'King of Rome' was given a glitzy funeral on the outskirts of the city in August.
And he is routinely lambasted over the capital's crumbling infrastructure, a legacy he inherited after years of inadequate investment.
Even Pope Francis joined the attacks after Marino flew to the United States to join the last leg of his recent tour, pointedly revealing that the mayor had not received any invitation from the Vatican.
Francis has is thought to have objections to the mayor's support for gay marriage and euthanasia.
But quite why the keen cyclist and former liver transplant surgeon is subject to such ire from across the political spectrum and the media remains something of a mystery.
His supporters suspect a concerted smear campaign linked to Marino's role in exposing a criminal network with links to the far right which had infiltrated itself into the municipal authority under his predecessor.
Police dismantled the "Mafia Capitale" network last year and dozens of local politicians and businessmen suspected of rigging tenders and siphoning off millions of euros destined for public services are due to go on trial next month.
But the mayor's critics say he is simply not up to the job and some have pointed out that "Dinnergate" is not the first expenses scandal to engulf him.
In 2002, Marino resigned as director of a transplant centre in Sicily after being accused of submitting the same expenses claim to both the centre and its US partner, the University of Pittsburgh Medical Center.