In the letter addressed to Woodhead, Parker said he would decide on what action, if any, to take after he received advice after the investigation was completed.
"For the avoidance of doubt (and because the media is likely to ask), it is not my intention to replace the ORC with commissioners," he said.
He recognised the issue was complex and not of "your council's immediate making".
"However, this issue remains unresolved after 30 years and I want to do what I can to help."
The investigation would focus on whether the council "has, or will have" the appropriate framework in place to consider applications for new permits before the old ones expire.
"It will also look at what support the council might need to achieve this."
Woodhead said it faced a "unique water management challenge, with hundreds of deemed permits arising from 19th-century mining operations due to expire in 2021".
"We have a plan in place to work through this. Hon David Parker, the Minister for the Environment wants to make sure we are on track, and has appointed Peter Skelton to look into this.
"We will of course cooperate with this investigation and show what we are doing to meet our obligations under the Resource Management Act.
The report leaked to the ODT last month said despite the change being on the radar for many years, "steps have not been taken" to ensure there was sufficient knowledge and capacity in its team to handle the applications, it said.
"In our view the council is ill prepared to process the impending volume of complex deemed permit replacement applications that will be lodged over the next two years."
The deemed permit replacement work has been one of the council's most high profile and contentious projects.
The report said there was no clarity as to what minimum flows were likely to be in respect to these applications.
Council staff also seemed unsure how many applications it would receive. Individuals indicated the volume could be anywhere from 100 to 1000 consents.
