A spokeswoman for National said whether or not the Party will vote for the bill will be discussed in caucus tomorrow morning.
Last week, Ardern announced the Government will be rushing the bill through the House.
Ardern wants to get to the bottom of why fuel prices are so high and took aim at petrol company's high margins as one of the main reasons.
She said "consumers are being fleeced" at the petrol pump.
Ardern today said if National think the almost 40c a litre increase in fuel prices in the last year warrants an investigation – "they need to support this bill in its second reading."
National Leader Simon Bridges has been critical of Ardern's approach to outlining how much tax the Government is taking at the pump.
Last week she said of the 39c a litre petrol prices have increased between October 27, 2017 and September 28 this year – just 6.8c of that was due to an increase in taxes over that period.
That increase is made up of a 1.77c increase in Emissions Trading Scheme (EST) taxes and 5.04c of GST over the same period, Ministry of Business, Innovation and Employment (MBIE) data shows.
But it does not include the 3.5c excise tax, which came into effect September 30, or 10c a litre Auckland Regional Fuel Tax.
On Friday, a Spokesman for the Prime Minister said Ardern's comments were "based on the most accurate information (MBIE) had compiled at that time."
"She was clear that the figures she was using were accurate as at that time and were through to 28 September 2018."
She doubled down on this at post-cab today.
"I was explicit about the data I was using – it was the most up-to-date figures I was using from MBIE."
Asked by the Auckland Regional Fuel Tax was not included in the 6.8c figure, she said that is a "question we have asked of the Minister of Business, Innovation and Employment (MBIE.)"
She said they are working on modelling that will include that regional fuel tax at the moment.