"This is exactly why we need a review of what has happened up until this point, which we have committed to doing independently, informed by the review of the Ministry of Health."
The council's priority was working with the SDHB to support the affected communities, and focus on identifying the source of the problem so it could be fixed, he said.
Hawkins did not say whether he still stood by his comment to Checkpoint.
Dr Jack told RNZ the SDHB's advice was to increase testing, but not that the city council should not go public.
"For a one-off exceedance, the recommendation and guidelines are to increase the testing to work out if there's a possible reason why it was elevated and then if there are obviously more results, then action would be taken," she said.
"Our recommendation was to increase the testing. We didn't advise that they shouldn't go public. But the usual process is that you would not go public with that information if they're following the recommendations of increasing the testing and working out what's going on."
As for any plans to change that process, Dr Jack said the Water Services Bill that would support the new drinking water regulator was out for consultation and that was likely to be an area closely looked at.
More than 1000 people have had their blood tested for lead contamination since the no-drink notice was issued, with a community testing clinic in place in Waikouaiti from Tuesday until Friday.
Results have already started returning, with residents describing a mix of relief and confusion.
The World Health Organisation states on its website there is no level of exposure to lead that is known to be without harmful effects and lower exposure levels could still cause health problems.
Dr Jack said the SDHB was using an internationally accepted threshold for lead blood levels that the New Zealand guidelines were going to be using, just as a cutoff for its management.
"We're not planning to reconsider that threshold. Anyone above that 0.24 gets a call from our public health unit and a detailed discussion about what their possible exposures may be," she told RNZ.
- Additional reporting RNZ