The requirement was endorsed by the Gisborne inquiry into the under-reporting of smear abnormalities.
The rule forced some community labs, and public ones serving Waikato, Wellington and Dunedin hospitals, to pull out of cervical screening and send slides to other laboratories.
Auckland Hospital and Christchurch Hospital had until July to reach 15,000, but are considered unlikely to meet the target.
The screening unit spokesman said they would not be forced out of cervical slide reading.
A public hospital laboratory presence in the programme was important for academic pathology, for training, and for sustaining the pathology workforce.
But 13 laboratories reading 440,000 slides a year - on average just over 33,800 each - might still be too many.
Fewer laboratories reading a greater number of slides contributed to a high level of expertise in laboratories and a high-quality result for women.