Rouhani's government has launched an investigation into public pay following the reports of executives at the state insurance regulator earning more than 50 times the base government salary.
The president's opponents are demanding answers on behalf of struggling Iranians who have yet to see the promised economic benefits of the country's nuclear deal with world powers.
The Iranian parliament's conservative speaker, Ali Larijani, hammered the message home in the legislature yesterday, announcing the Supreme Audit Court would release a report on the issue next week.
The disclosures surfaced two months ago, when the salaries of several senior executives at the Central Insurance of Iran (CII), the state insurance regulator, were disclosed on social media.
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In some cases the salaries ranged between 700 million and 800 million rials (USD 20,000 to USD 23,000) per month.
The source of the leaks is not known but several Iranian media picked up on the reports, including IRIB state television which wrote on its website that the disclosures had "shocked and angered ordinary people".
"I am ashamed that under my responsiblity an incident... became the target of massive media attacks on (the CII), you and the government," Mehr news agency quoted him as writing in a letter to Rouhani.
With anger mounting over the dislosures, Rouhani on Sunday ordered first vice president Eshaq Jahangiri to conduct an investigation into senior officials' income and bonuses.
Government spokesman Mohammad Bagher Nobakht even offered "apologies to the people" over the salaries. He said loopholes that allowed for excessive pay would be closed and that officials who received such wages would "certainly be removed from office".