National's finance spokeswoman Nicola Willis has written to Finance Minister Grant Robertson asking him to re-open discussions for an entity that would cost policies.
Labour and the Greens had been keen on such an organisation, and promised one at the 2017 election.
Robertson's model for such an office was to create an Officer of Parliament, which would be responsible to MPs, rather than to the government of the day. This was to give opposition parties confidence their policy proposals would not leak while they were being costed.
But creating an Officer of Parliament required the consensus of opposition parties. In 2019, then-Leader of the Opposition Simon Bridges refused to give his support to the proposal and it died.
But National, whose 2020 election campaign was beleaguered by allegations of poorly-costed policies, has since changed its tune.
On Friday, Willis wrote to Robertson, CC'ing other party leaders asking for Robertson to "commence discussions to progress the establishment of an Independent Budget Office".
"The function of this office would be to provide independent, expert advice to Members of Parliament on the costs of proposed policies and election manifesto commitments," Willis said.
Willis gave some backing to Robertson's preferred model, saying that "genuine independence" would best be achieved "through an Officer of Parliament model", although she said National was open to "considering a transition phase to such a model".
She added it should have a clearly defined mandate, minimise cost to the taxpayer, and have protocols to ensure confidentiality.
The Officer of Parliament model has a significant detractor: the Speaker of Parliament, Trevor Mallard.
Mallard has criticised the model because it differs from other officers like the Auditor-General and the Ombudsman, which are tools to hold the Government to account, rather than to hold political parties accountable for their costings.
Earlier this week, Mallard reiterated these remarks in tweets.
"An Officer of Parliament model is inappropriate. The real officers - Auditor General and Ombudsman are positions designed to hold government to account. This office isn't," Mallard said.
Robertson's office has received the letter and had no further comments to make.
Earlier this week, Robertson said it was too late to fund the creation of such a unit, but he was open to looking at it in future.
"Last term the Government sought broad political support to ensure our proposed IFI had institutional credibility when established, but no consensus could be reached on its formation. The National Party as the major opposition party at the time expressed the view that it would not use the unit if we tried to establish it before the 2020 election," Robertson said.
"I note the change in position expressed by the National Party. I continue to be interested in to exploring the option of establishing an institution, as resources and other priorities allow, but regrettably it is too late to be considered as part of Budget 2022," he said.
Willis said she was hopeful the unit could be established before the 2023 election.