The independent Climate Change Authority is engaged in a public war of words with the environment minister, Greg Hunt, over the government’s assertion that “Labor’s climate policy” would impose a “$600bn carbon bill”, saying the claim is “weird” and “misleading”.

The prime minister on Tuesday unveiled a new greenhouse gas reduction goal of reducing emissions by between 26% and 28% of 2005 levels by 2030.

One day before that announcement, the Daily Telegraph revisited modelling done in 2013 for the CCA of a 40 to 60% emissions reduction target, in a front-page story headlined “ALP’s $600bn carbon bill”. The paper argued the cost was attributable to Labor because the party has said it would base its long-term targets on up-to-date advice from the CCA. Labor has not yet announced its preferred 2030 target.

Abbott then used the same figure to claim Labor’s policy would “hit our economy with massive and unmanageable costs, massive increases in power prices, massive increase in the hit on families’ cost of living”.

But in a statement released late Friday, CCA chairman and former Reserve Bank governor Bernie Fraser said: “Others have wrongly claimed that the authority’s own modelling shows that the 40 to 60 target would impose very high costs – in the order of $600bn – on the economy. This is not correct.”

Within half an hour Hunt had issued a retaliatory statement, saying “the modelling clearly shows the cumulative hit to GDP from Labor’s carbon tax would be more than $600bn by 2030 in nominal terms”.

In an interview with Guardian Australia on Saturday, Fraser insisted the government’s assertion was wrong.

“Some people who don’t understand modelling draw inferences that really can’t be drawn,” he said. “This is a good illustration of the difficulties modelling can create when misinterpreted to derive misleading meanings.”

“This $600bn figure is not drawn from any logical process and it becomes weirder and weirder the more that you look at it. It compares a scenario where Australia has a 44% target by 2030 and the rest of the world is taking very strong action, with a scenario where Australia has no target and does nothing and the rest of the world does very little, almost nothing at all. It is the inferred cost difference between those two scenarios.

“If you wanted a figure with some logical credibility or relevance you would model the cost of the government’s 26% target and a 40% target for 2030 and look at the difference between those two.”

In fact the government has received modelling of the economic cost of its own target and a target similar to the one it asserts Labor will adopt.

That modelling, by leading economist Warwick McKibbin, showed the 26% target would shave between 0.2% and 0.4% from Australian GDP in 2030, but the same modelling found that based on similar assumptions, a 35% target would cut only 0.3% to 0.5% and a 45% target would cut between 0.5% and 0.7%. The $600bn figure is based on a GDP cost in 2030 of over 2%.

The government has not yet released that modelling, but says it will do so in coming days. It had intended to abolish the CCA but could not get the support of the Senate to do so.

Fraser also said the government’s new target is not “in the middle of the pack” of similar countries, as the prime minister has asserted, but rather “at or near the bottom of the group of countries we generally compare ourselves with”.

Fraser said with the “right” policies the authority was confident “more ambitious targets than those adopted by the government can be achieved at modest costs”.

Under the deal the government did with the Palmer United party to pass its Direct Action policy, the CCA has been asked to look at alternative climate policies.

But Fraser says it is difficult to do that assessment while the government makes false claims about emissions trading schemes every time they are publicly mentioned.

“The authority’s current work on the case for a market-based ETS for Australia is obviously occurring in a difficult environment,” he says.

“While part of the minister’s terms of reference to the authority, the very idea of an ETS (and those raising the idea) are criticised by government members every time it surfaces, asserting it is a ‘tax’ (which it is not in substantial respects), which will have major economic and social consequences (which is not the experience of those countries where ETSs are prominent components of their climate policy tool kits).

“Major decisions are looming as to how the inevitable costs of achieving large reductions in emissions are best funded – through, for example, expansion of the government’s Emissions Reduction Fund activities, which are financed directly from the budget, and/or through market-based mechanisms like an ETS. However this conundrum is eventually resolved, substantial shifts in much of the current thinking and rhetoric around these issues can be expected,” he says.