The initial cut skipped this analysis, despite the fact it might have qualified for it. Analyses were completed after the fact.
The policy was initially set to expire after just three months, but has been extended twice thanks to the cost of fuel remaining high.
Wood said the most recent extension of the cuts, which will see them expire at the end of January 2023, was put through an emissions analysis which showed they would increase emissions
"It didn't meet the requirements under the formal Cabinet note but nonetheless we have done an assessment as to the impact there.
"There is a small overall impact [to emissions] which is assessed as a result of the reduction," Wood said, "but overall of course in terms of our emissions reduction programme work it was relatively small".
"This is one of those situations where we've felt the financial pressures were very pressing on many New Zealanders as a result of the global energy shock so we took action, at the same time it was important we understood what the impact of that might be so we could assess against the broader programme what the emissions impact of that might be," Wood said.
He added the Government was still on track to hit transport emissions reductions goals for the Government's first emissions reduction budget, which takes in the period between this year and 2025.
He said the policy would not "materially change" the fact New Zealand was on track to hit this target.
There are questions over how the Government will eventually taper off the cuts and return to the full level of tax, which is spent mainly on maintaining roads and building new ones.
The Green Party's transport spokeswoman Julie Anne Genter said her party did not support the extension of the cut, which will have cost more than $1 billion by the time it expires at the end of January.
"We can and must respond to the current cost of living challenges in away that allows us to address the climate crisis. Otherwise we are never getting off this fossil fuel treadmill and there will be dire consequences for human wellbeing," Genter said.
"There are much better ways to spend over $1 billion to help those who are struggling with high petrol prices. Increasing benefits or providing higher cash payments to those on low incomes would allow them to buy what they need, including petrol if they do rely on it.
"The petrol tax cut also benefits those on high incomes, and ultimately does nothing to transition us away from fossil fuels," she said.
Genter said the Government should "invest in clean, reliable buses and trains, including regional passenger rail, which reduces our transport system's dependency on oil".
The question is mainly whether the Government can afford to continue with the full level of subsidy or whether it will taper it off slowly.
Wood said it was "exceptionally difficult" to taper off road user charges, which were set based on a complicated calculation relative to the level of fuel taxes.
"It would potentially lead to relatively serious gaming of the system as well," Wood said.
There are persistent concerns people could game the road user charge system by buying large quantities of the charge at the lower rate with the intention of using them when the cost of the charges was put back up.
