Under all settings in the traffic light system taxi services are prohibited from asking passengers for a vaccine pass. Face coverings are required under red and orange settings.
If the government would not change the settings, the small passenger service industry should be removed from the "transport" portion of the traffic light system, Quirke said.
"This would enable our member companies to form their own policies regarding vaccination requirements in line with their own risk assessments, health and safety compliance, and human rights requirements.
"It would also align us with the many other responsible businesses who have had the ability to implement their own policy to protect their people and customers."
Ten days after sending that letter, Quirke had still not received a response from the government.
The Ministry of Transport has its own policy which will not allow unvaccinated people on any of its premises.
"Seems quite ironic that they have the ability to put in that policy and we don't," Quirke said.
Drivers were happy to take passengers who had a legitimate exemption, but were not willing to be in close proximity to those who had made a personal choice not to be vaccinated, he added.
"We are being forced to provide a service to those that consciously refuse to protect themselves and others, willingly threatening the safety and wellbeing of our communities."
Covid-19 response minister Chris Hipkins has been approached for comment.