NSW Premier Chris Minns and Attorney-General Michael Daley have been urged to reconsider the ex gratia payment offered to Kathleen Folbigg.
Ms Folbigg was jailed in 2003 over the deaths of her four children before being freed in 2023 after new scientific evidence cast reasonable doubt over her convictions, which were later quashed.
Mr Minns said the $2 million was taxpayer funds and did not come from a "magic pot".
"This was the most amount of money that we believed we could allocate ... without pulling it away from other important programs," Mr Minns said.
Compensation has been paid to others in the past after legal action and Mr Minns said Ms Folbigg was free to sue the government.
Mr Daley announced the payment on Thursday, more than a year after a compensation claim was submitted.
After telling reporters the payment was offered to close down a push for a parliamentary inquiry, Nationals MP Wes Fang said the government was seeking to avoid scrutiny.
"It wasn't a coincidence," he told AAP.
He said the $2 million was a "round figure" and the government had not revealed any information on how it was calculated.
"That raises concerns that there's been no evidentiary basis for that offer - it's just been plucked out of the air," Mr Fang said.
He said the push for an inquiry was more important than ever.
"Mainstream everyday Australians have found the figure to be quite an affront," Mr Fang said.
"There's a growing call to understand how there's been the assessment done, and what assessments have been done."
Greens MP Sue Higginson said the issue went beyond Ms Folbigg.
"It's very rare you get such a serious failing of the legal system and you get wrongful conviction and incarceration to this degree, but to suggest it will never happen again is just wrong,'' she said.
"It will, and we need a system of credibility with a bit of integrity about how we are going to address these injustices."
Ms Higginson accepted the budget had constraints.
"But I know there's room in the budget right now to give Kathleen something more than $2 million, something more commensurate with the harm that the justice system has perpetrated," she said.
Ms Higginson wrote to the premier and attorney-general on Friday, saying it remained "immensely challenging" to understand how the figure was calculated and urging them to review it.
"I also implore you to meet with Ms Folbigg and her team in negotiating an offer of ex gratia payment that reflects the extraordinary nature of this case," she wrote.
The premier and attorney-general are due before budget estimates later in August while calls for an inquiry into the payment could be furthered when parliament resumes in September.
