CCS Disability Action manages and issues permits, and advocates to improve the scheme.
Doctors or GPs assess people to determine their eligibility and local councils provide and monitor on-road parking spaces.
The New Zealand Transport Agency manages the legislation around parking requirements and fines.
More than 100,000 permits were issued under the mobility parking scheme last year.
"We believe that the rules should be extended to private areas and we're pleased to see this view supported by the bulk of those we surveyed, " said Mr Matthews.
"Many retailers are doing a fantastic job of providing, monitoring and enforcing use of these carparks. With such high numbers of people affected by access issues, it's not only a social but an economic issue for them," he said.