Tesla is quitting Australia’s main auto industry lobby group and has asked the consumer watchdog to investigate what it says are the organisation’s “demonstrably false claims” about the impact of the Albanese government’s clean car policy.

In a letter to the Federal Chamber of Automotive Industries (FCAI) on Thursday, Tesla said it had serious concerns about the lobby group’s public claims that the government’s proposed vehicle efficiency standard would significantly push up the price of most popular cars and utes, and significantly reduce the price of Tesla models.

Guardian Australia revealed on Wednesday that Tesla had used a submission to the federal government to accuse the FCAI of representing only those car companies that wanted to delay action on the climate crisis, and not members that backed Labor’s position.

The Australian arm of Elon Musk’s electric car company said FCAI had argued for a policy design that it described as “ambitious” despite knowing it would not cut vehicle emissions before 2030, and could lead to a substantial increase in CO₂. It also said the lobby group had told media outlets that the government’s policy could increase the price of popular utes by up to $13,000 next year but knew this was not how the system worked.

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In the letter on Thursday, Tesla asked the FCAI to publicly correct its “false claims” and acknowledge they do not accurately reflect what car companies intend to do.

Tesla said it had asked the Australian Competition and Consumer Commission to investigate claims by the lobby group that it believed were “likely to deceive Australian consumers”. It said it would no longer be an FCAI member after the 2023-24 financial year. Its company director, Thom Drew, had been a member of the FCAI board until this week.

Responding to Tesla’s accusations earlier this week, the FCAI said it had encouraged successive governments to introduce an efficiency standard for more than a decade, and that its members “want to continue to play their role in combating climate change and providing Australians with the zero and low emission vehicles they can afford”.

The lobby group said it stood by its analysis of how vehicles sold in 2023 would be affected by the government’s preferred policy if last year’s sales patterns were repeated next year. Its claims that the price of the most popular petrol and diesel cars would jump by thousands of dollars has been embraced and repeated by the federal Coalition as it has attacked Labor’s policy as a “family car and ute tax”.

FCAI was asked for its response to Tesla’s letter.

Independent analysts have said an efficiency standard is likely to have a much smaller impact on the price of new cars than FCAI has suggested. The Grattan Institute estimated the policy would on average increase prices by about 1%, but that consumers would quickly be financially better off due to significant savings on fuel and maintenance costs.

An efficiency standard requires car companies to meet a per kilometre emissions target averaged across all the new cars it sells in a new year. The target would lower each year. Under the government’s preferred model it would be cut by 60% by 2030. Suppliers can choose which cars they sell, but would need to offer enough fuel-efficient models to offset more polluting vehicles to meet their target.

Companies that emitted less than the required average would be rewarded credits that they could sell to cars that were above their average. Alternatively, companies that missed the required average could pay a penalty or make up the difference by selling more clean cars over the following two years.

Most developed countries have some sort vehicle efficiency standard. The government’s preferred design has been supported by some car companies, including Volkswagen and Hyundai, but some others, including Toyota, want it changed and delayed. National CO₂ emissions from transport in Australia have increased by nearly 20% since 2005.

Tesla’s submission included a critique of calculations the FCAI has given to media outlets that suggested the government’s preferred model would substantially push up the price of 18 of the country’s 20 top-selling car models. It said the FCAI had:

• Based its calculations on the most polluting type of each car model only. For example, when looking at the Ford Ranger it chose only its most polluting variant, the Raptor, which emits 262 grams of CO₂ per kilometre. But the government’s Green Vehicle Guide last year listed 42 variants of Ranger, including 20 that emitted less than 200g/km.

• Misrepresented how an efficiency standard would work. It chose the most polluting variants of each car make, calculated how much they would emit above the allowed average, multiplied the difference by $100/g – the proposed penalty price – and added this amount to the car’s sticker price. In reality, penalties would not be applied to individual cars and companies would be expected to increase their range of clean vehicles to offset more polluting models.

• Falsely claimed two popular Tesla EV models would each fall in price by about $15,000 next year without checking with the company if this was the case.