Australian fossil fuel exports are comparable with those of the United States, which has 13 times the population and a gross domestic product that's 15 times bigger.
Indonesia, Canada, Iraq, United Arab Emirates and Qatar export less fossil fuels than Australia.
Among developed economies, Australia is the biggest producer and exporter of fossil fuels based on CO2 potential, and second only behind oil-rich Norway on a per capita basis.
Homegrown exports are almost three-quarters the size of all European Union nations combined.
The report found Australia is the world's largest coal exporter, responsible for 29 per cent of the world trade, a figure outstripping Indonesia with 26 per cent and Russia's 14 per cent.
In absolute terms, Australia ranks fifth as the biggest miner of fossil fuel carbon, 10 times the world average per capita, and behind only China, the US, Russia and Saudi Arabia.
"On any reasonable assessment of domestic emissions alone, Australia is a large emitter and Australia's emissions are rising, not falling," the report's author Tom Swann concluded.
The study found Australia's domestic greenhouse gas emissions are higher than 40 countries with bigger populations, making it 14th globally.
Prime Minister Scott Morrison last week resisted pressure from Pacific nations to include a transition away from coal towards renewable energy in the Pacific Islands Forum communique.
But The Australia Institute's report found the nation's role in fuelling the "climate crisis" was far greater than even rising domestic emissions would suggest.
"Australia has the opportunity, and obligation, to face up to the climate crisis through policies to limit its carbon exports, starting with a moratorium on new coal mines," the report said.