Prime Minister Jacinda Ardern and her deputy Winston Peters have paid back allowances of more than $21,000 which they were wrongly paid because of a government department's error.

They've received an apology from the Department of Internal Affairs, which says they didn't claim the allowance.

They continued to receive a Wellington accommodation allowance after they moved into official residences following the formation of the new government.

It should have been stopped as soon as they moved.

"As soon as we were advised of the error we both immediately took steps to reimburse the money. That has now happened," they said in a joint statement on Tuesday.

Ardern repaid $12,205 and Mr Peters $9123.

"While mistakes happen, we have accepted the officials' apology," they said.

"Appropriate use of taxpayer money is something we both take extremely seriously."

Peters was embroiled in a scandal during the election campaign over his pension payments after it was revealed he had been overpaid for several years.

He paid it back as soon as he was told about the mistake.

- NZ Newswire