The Privacy Commissioner is calling for the DNA information of nearly two million New Zealanders to either be destroyed eventually or transferred to another agency.
Consultation is being held on the privacy, storage and use of newborn blood spot cards, known as the Guthrie cards.
Almost every baby born in New Zealand since 1969 has had a blood sample taken from their heel to screen them for preventable disorders.
The data is kept indefinitely by the National Screening Unit.
However, Privacy Commissioner Marie Shroff says that is risky, as it could be used inappropriately.
Ms Shroff suggests either destroying the data after 16 years or keeping it in the control of a separate agency, governed by strict legislation.
The National Screening Unit says many views are being assessed as it develops a policy.