However, both it and AIA New Zealand say they would be ready to work with the government to improve health outcomes for Kiwis.

“There has to be appetite from the government to go that way. And we don't see that,” a nib spokeswoman said.

AIA NZ chief executive Nick Stanhope says the health system is facing “some big challenge” as the aging population grows.

“New Zealanders are increasingly needing support to manage their everyday health and wellbeing as well as respond to health issues which might arise,” Stanhope says.

“At AIA NZ, we believe [the] private sector can work together with the government to help improve health outcomes for New Zealanders and relieve pressure on the public health system,” he says.

“For example, we can see the value in improving and incentivising access to private health insurance to help take the load off the public system and ensure it has capacity for people who need it most.”

Stanhope says as one of the largest life insurers in the world, AIA is well-placed to explore what works well in other markets.

He says an approach to encourage people to make lifestyle improvements and take preventative measures is also something AIA can help with.

Newly appointed nib NZ chair Hanne Janes says that “there is certainly huge strain on the public health system and innovative ways need to be investigated to change access to health delivery, improve outcomes and innovate in the area of funding.

“nib is committed to working with government and third parties to try to identify what can be done differently.” nib is sponsoring the NZ Initiative's health summit scheduled for August this year.

A 2014 paper by NZIER found that making health insurance premiums tax deductible would probably create “a fiscal hole” for the government because the cost of subsidising those who already have health insurance would likely outweigh any benefits.

However, that paper looked at a range of measures that could be adopted by the government, including levying those with high incomes who don't have private health insurance or using an employer-based system which automatically enrolled employees into a health insurance scheme but allowed them to chose to opt out, in a similar fashion to how KiwiSaver works.

GoodReturns asked both Southern Cross and Partners Life to comment on whether NZ should make health insurance premiums tax deductible but received no response.