Parker said he was advised that the Ministry "identified the members of the group based on their expertise on waste minimisation and circular economy initiatives, and that Ministers had no involvement in the selection process".
He said the Ministry was "looking into the internal process that was followed" and that he expected the Ministry to provide him with "an update on its findings and identified areas of improvement".
Brown said that the "fact that the Ministry for the Environment is conducting an internal inquiry into the appointment of three of Mahuta's family to a five-member waste working group justifies why it is important National has been asking questions about this appointment process and the perceived conflict of interest which exists".
"New Zealanders have clear expectations that any conflicts or perceived conflicts are managed appropriately and the appointment of three of Mahuta's family members to a five member waste working group raises serious questions about a perceived conflict of interest".
Gannin Ormsby has been approached for comment.
Mahuta's office pointed to a previous statement from the office on contracts to family members.
Relating to matters where Minister Mahuta has ministerial responsibility, a spokesperson for her office then said: "Where there have been conflicts they have been disclosed to the Cabinet Office. Where there have been conflicts, they are managed appropriately, in accordance with the Cabinet Manual."
Parker's office said that procurement documents included full disclosures of potential conflicts of interest, and that all payments for work were at a standard market rate and expenses were pre-approved.
The Ministry also sought advice from the Public Service Commission before the contracts were signed and there was an explicit understanding that arrangements might need to be reviewed if Mahuta were to take on any ministerial responsibility for waste matters in future.
There were also regular meetings to discuss any potential risks and mitigation as they arise.
Prime Minister Jacinda Ardern said she was confident the Government had followed advice around potential conflicts as set out by the Cabinet Office.
"We stick closely to the guidance of the Cabinet Office as all Governments are expected to do and that guidance has been followed," Ardern said.
"I'm confident the advice has been followed," Ardern said.
Brown said he expected the results to be made public when the ministry concluded its review.
All contracts had been awarded in line with Government procurement rules.
Brown said the existence of the review vindicated the fact he had asked questions.
"National will continue to be asking questions about these issues," he said.