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The advice is contained in a just released regulatory impact statement (RIS) by officials from the Ministry of Business, Innovation and Employment.
It was previously known that officials opposed the move, but the estimated cost to the Government is new.
But Energy Minister Megan Woods contests the estimates.
Her statement on the bill, says the modelling by officials was based on a GNS report for inputs and the report itself expressed caution about relying on resource estimates, saying "this study attempts to qualify what is almost unquantifiable."
Woods' statement also said the model used for estimating the cost was unable to take into account any potential from existing exploration permits, covering 100,000 sq km.
The new advice has been released alongside the Crown Minerals (Petroleum) Amendment Bill which gives effect to the ban announced in October by Prime Minister Jacinda Ardern, Regional Economic Development Minister Shane Jones and Climate Change Minister James Shaw.
The ban in April took the industry by surprise because it was not part of any confidence and supply or coalition agreement and had not been explicitly promised by Labour during the election campaign.
However Ardern said it was an important step to address climate change.
She promised that the existing 31 permits covering an area of 100,000 square kms would be protected and said they could run as far out as 2030 could go an additional 40 years.