On the Winter Energy Payment, the Auditor-General said MSD had: "made payments to recipients whose circumstances are expressly excluded from eligibility under the Act".
In a statement to the Herald, MacPherson said when the legislation passed in 2017, it "didn't fully align with the policy intent of who should be paid – meaning the WEP didn't cover everyone it was meant for".
"There was an error in drafting the legislation and it wasn't picked up in time to be corrected during the legislative process."
The error meant that 25,760 people – or 3.3 per cent of the 774,200 people who received the WEP – were collectively paid $3.4 million they were not entitled to.
People who received Government funding for long-term residential care or residential care services, but were not eligible for subsidies in those areas, were mistakenly paid the WEP.
As were people who were absent from New Zealand for more than four weeks during the time the WEP was paid out.
MacPherson said the Government was in the process of fixing these issues with a bill, expected to pass in May, which would ensure people are "lawfully able to be paid the WEP as originally intended".
But he said MSD would not be seeking to recover the payments.
"Although unauthorised, payments were consistent with policy and were at no fault of the people getting the WEP."
When asked about the error, Sepuloni said: "You never want to make mistakes, but we're not the first Government that's had a drafting error".
"This is a drafting error under us, there have been drafting errors under previous Governments – it's always disappointing when a mistake is made, but you fix it as quickly as you can."
National's Social Development spokeswoman Louise Upston said that because of "Government incompetence," $3.4m was paid out illegally to more than 25,000 people.
"Now the Government is trying to rush through changes to fix this, it needs to make sure that this is fixed properly now, so more taxpayers money isn't thrown away."
The Auditor-General also pointed out issues with payments around the PGF, saying an "error in the paperwork" meant that "authority to spend could not be granted until the paperwork was corrected".
A spokesman for the Provincial Development Unit said in August last year, the Minister of Finance, Grant Robertson, approved funding for Ministry of Business, Innovation and Employment (MBIE) of $18 million to "ensure effective administration of the Provincial Growth Fund".
"MBIE incurred expenditure against this appropriation in good faith," the spokesman said.
But in mid-September, the Provincial Development Unit discovered that the August paper included an error which meant the approval of the funding was done wrong.
"The Minister of Finance approved the new appropriation on October 7 last year, correcting the previous error," the spokesman said.
Shane Jones, the Minister in Charge of the PGF, said this morning he was getting a briefing from MBIE about this issue.
"With a $3 billion fund, there is always going to be a bit of bump and grind in expeditiously allocating that fund and we have to be respectful of the Auditor-General's concerns."