Climate, health and vehicle groups proposed the changes as part of the government's consultation on a fuel-efficiency standard, submissions on which closed on Wednesday.
The standard, due to be introduced later this year, is expected to set a cap on transport emissions to encourage car makers to import more battery-powered vehicles.
Climate and Health Alliance chief executive Roland Sapsford said the law would be an important step towards improving air quality and health outcomes in Australia.
"Without a fuel-efficiency standard, Australians are exposed to dangerous air pollution and an array of serious health conditions, particularly in children," he said.
"Exposure to transport-related air pollution may permanently stunt lung growth in children under 15 years, leading to other cardio-respiratory impacts throughout their lives."
The alliance wants the government to set a limit of 95 grams of carbon emissions per kilometre for new vehicles from mid-2024.
The limit, it said, should be raised annually until transport reached zero emissions by 2035.
Mr Sapsford said the 95-gram limit, which would match current European rules, would help reduce the prevalence of asthma and other respiratory conditions.
The Australian Electric Vehicle Association echoed the call for a 95-gram limit from next year, with national president Dr Chris Jones saying the cap should apply to all light vehicles under 4.5 tonnes including dual-cab utes and four-wheel drives.
"Australia is really starting from way behind on vehicle emissions so we have a lot of work to do," he said.
"This standard will give automotive companies the guidance they need to achieve a zero-emission vehicle fleet by the middle of next decade."
Dr Jones said bold targets would be needed for Australia to catch up to progress in countries including New Zealand, which launched a similar standard in January.
While stopping short of naming an emissions limit, the Climate Council said Australia's fuel-efficiency standard should aim for all new vehicles sold to be "zero emissions as soon as possible and by 2035 at the latest".
All three submissions proposed significantly higher cuts than Australia's voluntary targets, set by the Federal Chamber of Automotive Industries, which aim to cut emissions to less than 100 grams for cars and less than 145 grams for heavier vehicles, such as utes and SUVs, by 2030.
Data showed the automotive industry missed its target for large vehicles last year, with emissions rising to 212.8 grams, exceeding the industry's 189-gram target.
The federal government committed to introducing a fuel-efficiency standard in Australia after it launched its National Electric Vehicle Standard in April.
Transport Minister Catherine King said she intended to produce "an exposure draft of legislation" by the end of the year, with plans to introduce it to parliament this year or early next year.
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