Labour is working with the government to correct an error made by Work and Income that meant beneficiaries were underpaid for many years, the party's leader says.
Work and Income has paid most benefits a day late for almost 20 years and some beneficiaries are now getting their money in back-pay.
Parliament is expected to pass a law under urgency this week to retrospectively change the payment date to the day after stand-down.
Labour leader Andrew Little said the party had put a proposal to the government to have a six-week process for people to apply to be back-paid.
"Not everybody will apply because many people won't feel the need for it but there will be some who will be out of pocket and will feel that, and should have the opportunity to make good that loss.
"We've put that up - we intend to put that up during the debate on the legislation."