The Government is facing pressure from the Greens who are demanding ACC divest almost $1 billion from fossil fuel investments.
The party says ending state-sponsored investment in the industry is the next step for climate action.
Green MP Chlöe Swarbrick told Newshub if ACC is unwilling to step up, the Government should.
"There is about $920 million vested in fossil fuels, and I, as a Green Party MP but also as a New Zealander who cares deeply about the planet, think that it is grossly irresponsible.
"There is absolutely a place for a Government that is talking about showcasing leadership in climate action to ensure our Crown entities that are investing New Zealand money should be doing that."
ACC controls around $40 billion worth of investments. The Government-owned entity already has a list of areas which it avoids investment in for ethical reasons, including tobacco, land mines and automatic or semi-automatic firearms.
However, according to its website, "ACC's ethical investment policy does not exclude investment in carbon-intensive businesses".
"If Parliament changed the law banning use of fossil fuels, ACC would stop investing in the production of fossil fuels. Fossil fuel producers would be added to our exclusion list."
In May, The Government passed its Zero Carbon Bill, which lays out a 30-year plan aimed at limiting global warming to no more than 1.5degC.