Parliamentary Commissioner Simon Upton says van Velden was "incorrect and misleading" when she said on TVNZ's Breakfast show that the commissioner has concluded the ban on offshore exploration for oil and gas would likely "increase global emissions".
Upton's letter notes a similar comment appears in Act's energy policy.
Despite the letter being sent last week, the claim was still on the party's website this morning.
RNZ has approached Act for comment.
"I most definitely did not say that the ban would increase global emissions," the letter said.
The report did express concerns that the impacts of the ban were not fully analysed.
Overturning the ban was a policy of both Act and National, and the new government (made up of these parties and New Zealand First) has been criticised for it by green groups at the COP28 climate summit in Dubai this week.
Upton's letter ends with a suggestion that, after criticising the Labour-led government for not making a careful analysis of the costs and benefits of the ban, "It would create an excellent precedent if your decision to lift the ban followed a thorough analysis of the costs and benefits of such a step".
"Five years have passed since the imposition of the ban and much has changed since then."