Since coming to power in 2013, Hassan Rouhani, Ahmadinejad's successor, has sought to put Iran's economy back in order after it plunged into recession and was hit hard by inflation.
Tackling the handouts -- a partial replacement after subsidies on staples such as electricity, gas, water and bread were cut -- has proved politically difficult.
But Ali Rabii, Rouhani's minister of labour and social welfare, wrote in an open letter that change was needed as the bill for the individual monthly payments of 455,000 rials (about $15) was too high.
"We should face reality. Reforming the current allowance payment system is a major step toward increased social justice," he said, noting all Iranians receive the money whether rich or poor.
Accused of economic mismanagement, Ahmadinejad, in office from 2005 to 2013, used funds gained from a then high oil price to finance populist policies.
He spent Iran's petrodollars on the controversial scheme at a time when sanctions imposed as punishment for the Islamic republic's disputed nuclear programme deepened its economic difficulties.
Inflation soared to over 40 percent and the rial plummeted against other currencies, chiefly the dollar.
Despite repeated calls from Rouhani's government, which has cut inflation to under 15 percent, for affluent families to refuse the allowance only 2.4 million from a population of almost 80 million have opted out.
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Economy Minister Ali Tayebnia on Monday said national debt stood at about $88 billion, noting: "No one knows the exact figure."
Ahmadinejad, in two terms, "had $800 billion in oil revenue and gained $52 billion -- at the current exchange rate -- from selling assets. But all we have inherited is large debts," Tayebnia said.
Rabii said the subsidy reform plan ordered by Ahmadinejad "should have been based on people's eligibility," rather than being universal.
"To continue this system is not defensible with the current situation of the country," he added.
The slump in crude oil prices in the past year has hit Iran hard. The current budget halved reliance on oil sales to 25 percent.
Rabii, signalling the government's plans for reform, also said money spent on handouts was harming domestic production and investment.
"Since 2010, 500,000 people have lost their jobs in development projects," he said. "This is the result of raiding development funds in order to pay cash allowances."
Rabii's comments echo those of one of Rouhani's vice presidents, Mohammad Bagher Nobakht, who has cited a one third shortfall in the annual $19.5 billion needed to fund the handouts.
"We will have to eliminate a great number of people" from the payment list, he added.