Both Peters and Ardern have repaid the full amount.

Prime Minister Jacinda Ardern and deputy Prime Minister Winston Peters were both mistakenly paid over $21,000 for accommodation they didn't need.

The pair put out a press release on Tuesday afternoon explaining the overpayment, which resulted from the Department of Internal Affairs (DIA) continuing to pay them an accommodation allowance despite each moving into an official residence.

Ardern received $12,082.19 while Peters received $9123. They have both repaid the amount in full and received an apology for the error.

"As soon as we were advised of the error, we both immediately took steps to reimburse the money. That has now happened," the pair said.

"The error occurred when the DIA's Ministerial Services continued to pay each of us a Member of Parliament's Wellington accommodation allowance after they had moved us into official accommodation, at which point payments should have stopped."

Neither had asked DIA for the payment. The payments covered a period from November to February.

"While mistakes happen, we have accepted the officials' apology. Appropriate use of taxpayer money is something we both take extremely seriously, and we have set a high bar for ourselves and others."

The mistake came to light as DIA prepared for their proactive release of ministerial expenses. The pair were made aware on Monday evening.

Non-Wellington based MPs receive an accommodation allowance in order to cover Wellington housing costs.

Outgoing National leader Bill English claimed $32,000 in accommodation allowance while living in a Karori home owned by a trust in the late 2000s.

He paid it all back when media uncovered the allowance in 2009.

More soon.