The Labor party is promising to set up a royal commission into the failed Robodebt scheme before the end of the year if it wins the federal election.
The government rolled out the program in 2015, which used an automated system to determine if Centrelink recipients had been overpaid.
However, many people were wrongly accused of owing money.
A class action later found the Commonwealth had unlawfully claimed nearly $2 billion in debts from 433,000 people.
Of this, $751 million was wrongly recovered from 381,000 people.
Federal Court Justice Bernard Murphy described the scheme as a "massive failure in public administration" in June last year.
He approved a settlement worth at least $1.8 billion for people wrongly pursued by the federal government's Robodebt scheme.
If it wins the May 21 election, Labor is promising a royal commission would be asked to determine who was responsible for establishing the scheme, how much it cost and investigate the harm it caused, among other issues.
Shadow Minister for Government Services Bill Shorten said the inquiry was estimated to cost $30 million, which he said was comparable to investigations into bushfires and pink batts insulation deaths.
He said there are questions about the scheme that still need answers.
"We haven't yet got the missing piece of the puzzle," he said.
"The people have got their money back but the Australian taxpayer never had the satisfactory explanation. Why did Robodebt happen?"
Opposition Leader Anthony Albanese said Robodebt was a "human tragedy" and the inquiry would ensure there was not a repeat of the scheme in future.
"Against all evidence, and all the outcry, the government insisted on using algorithms instead of people to pursue debt-recovery against Australians who, in many cases, had no debt to pay," Mr Albanese said.
"It caused untold misery."
Prime Minister Scott Morrison said "the problem has been addressed" when asked if the Coalition planned to hold inquiries into the program.
"There have been numerous inquiries into this and there's been court matters which we've fully cooperated in, and almost $750 million in response to that," Mr Morrison said.
"And the changes in the scheme have been in place.
"So the problem has been addressed, but any such inquiry, I imagine, would have to start with the process of income assessment, averaging of income, which was introduced by the Labor Party."
