Scott Morrison could be investigated by a powerful parliamentary committee over his role in the robodebt scandal.
The Greens have called on Speaker Milton Dick to consider allowing the former prime minister to be referred to the privileges committee, which deals with matters such as contempt of parliament.
A royal commission into robodebt made several adverse findings against Mr Morrison, including that he "allowed cabinet to be misled" on the legality of the scheme when he was social services minister.
The scheme, which ran from 2015 to 2019 under the former coalition governments, used annual tax office data to calculate average fortnightly earnings and automatically issue debt notices to welfare recipients.
Hundreds of thousands of Australians were caught up in the debacle, which illegally recovered more than $750 million and was linked to several suicides.
Greens MP Stephen Bates said Mr Morrison had repeatedly made false statements on robodebt to parliament.
"(Scott Morrison) made statements in the House in relation to the robodebt scheme that have subsequently been shown to be false by the royal commission robodebt scheme," Mr Bates told parliament.
"(Mr Morrison) made statements that clearly contradict the findings of the royal commission."
Mr Morrison rejected the adverse findings against him and said they were "disproportionate, wrong and unsubstantiated".
He accused the Labor government of a "political lynching" and described the commission as a quasi-legal process.
His comments were slammed by Government Services Minister Bill Shorten who said Mr Morrison was trying to frame himself as a victim of robodebt when he wasn't.
Mr Shorten described the former prime minister, now a backbencher, as a bottomless well of self-pity with not a drop of mercy for all the real victims of robodebt.
Mr Bates said it was critical for parliament to hold the former prime minister to account.
"At no point did the member for Cook (Mr Morrison) report to the House that the robodebt scheme was implemented without legislative change and was therefore illegal," he said.
"It is fundamentally apparent that the House cannot hold a minister or indeed a prime minister to account if the relevant minister makes false statements to the House."
Mr Dick said he would consider the matter and would report back to parliament on his decision.
Parliament will have the opportunity to accept the findings of the royal commission regarding former ministers involved.
Mr Shorten is expected to bring on a motion for the lower house to express its deep regret for the scheme, apologise to victims and frontline Centrelink staff and commit to ensuring such an unlawful chapter in public administration is never repeated.
Mr Morrison is the only former minister singled out in the robodebt report who remains in parliament.
Alan Tudge and Stuart Robert resigned this year, sparking by-elections in their seats.
The Greens have previously sought to refer Mr Morrison to the privileges committee over the secret ministries saga.
The referral was ultimately not supported but Mr Morrison was censured by the parliament.
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