Prof Cox, a cancer screening authority, was commenting on the Parliamentary Review Committee's three-yearly report on the national cervical screening programme, which he helped peer review.
The report highlighted problems with data collection and programme monitoring, and described "severely dysfunctional" relationships between programme managers and health workers, Prof Cox said.
"It's quite a damning report, really, given the programme has been in operation for over 10 years and has had time to get these things sorted out."
There was potential for women not to be followed up quickly enough because of data gaps.
The review identified an urgent need to ensure colposcopy data in the national register was complete.
"This problem has been evident for a decade and there is a possibility that people may unnecessarily develop invasive cervical cancer when they have severe pre-invasive disease, if assessment and treatment was unduly delayed," Prof Cox said.
Colposcopy - a procedure for assessing and treating pre-invasive disease - was provided by a range of health providers in the public and private sector, and there was a lack of consistency.
The review suggested an overhaul of how the Ministry of Health contracted services for the programme.
Recommendations for improving relationships and communication should be adopted because it was crucial to the success of any screening programme, he said.
Programme monitoring was carried out in Australia, leading to a lack of "ownership" in New Zealand, which had the expertise to do the work.
Periods during which there was a lack of information about how well the programme was performing overall made it difficult to make improvements.
Associate Health Minister Tariana Turia, in a press release, said better leadership for the programme was "urgently required" .
