"It was unclear on both sides how the error had occurred leading to a small fortnightly overpayment.
"Suffice to say, we agreed there had been an error."
Peters said that within 24 hours "the error and overpayment had been corrected by me".
"I subsequently received a letter from the area manager thanking me for my prompt attention and confirming that the matter was concluded to the Ministry's satisfaction.
"I am grateful to the Ministry for their courtesy and the professional and understanding way they handled this error. Like the Ministry I believed the matter had been put to rest."
The Herald has contacted MSD for comment on questions including how much was overpaid.
Peters' statement comes after Metiria Turei revealed to the Green Party conference earlier this year she had committed benefit fraud while a solo mother at law school in the 1990s.
However, there is no suggestion in Peters' statement that his overpayment was a result of deliberate action on his behalf or deception.
Turei said she revealed her benefit fraud to highlight how difficult life is for beneficiaries, but eventually resigned as co-leader during fallout, including two Green MPs stepping down from the list in protest and media questioning of her family circumstances at the time.
New Zealand Superannuation payments are paid fortnightly and rates differ according to personal circumstances.
The more common rates of payment (before tax) include single living alone ($900.20), married, or de facto couple, and both partners qualify ($681.60) and married or de facto couple and only one partner qualifies ($645.56).
Peters told the Herald the overpayments were a mistake, and did not result from any deliberate action from him or deception.
"Otherwise MSD would have taken action ... they have the powers.
"What led to the overpayment was a mistake, and nobody knows why. You have a whole range, maybe six or seven ranges of payments for Super. And I'd have been on one of the very lowest ones, and I think I was one up from where I should have been."
The matter was complex and he only knew the rough amount of overpayments. He was asked for and made a repayment that accounted for the overpayments plus interest.
"I just said, 'give me the total figure and I'll pay it off immediately.'"
Peters would not disclose that amount, saying it was private.
"That is between me and the MSD. It is a private matter, just like the whole leak [to media] came out of IRD, which is a crime. That's the reality of it all."
Asked if he would follow that up with a complaint, Peters said he was too busy to worry about that but believed he was narrowing in on who leaked his information.
Peters said he did not consider disclosing the overpayments to the public when he learnt of the mistake.
"We couldn't identify how it was made. And therefore the only thing was, 'well, how can we fix it up?' Which we did."
