Some had tested at "above the safe blood level", RNZ reported.
Some of those included children.
Jack said it was "expected".
"Some people have come back with levels that are higher than the cut... it's not very common when we look at the whole population that was tested," she said.
RNZ reported that Jack would not be drawn on the total number of people who had returned high level results.
But she said "further investigation" was needed - particularly where children were concerned.
Children initially had a finger or heel prick test that was for screening.
"Then we need to confirm that," Jack explained.
All people with "concerning blood lead levels" were being contacted.
Jack said all possible risk factors and exposures they may have had would be considered.
"And then, especially for the children, we're offering a visit out to their home to look at whether there are any other environmental risks - so, is there lead paint, is there renovation, are they involved in hobbies, do their parents work in a place where there might be exposure to lead."
- RNZ