"To avoid further health and environmental disasters, governments must take heed of the science, listen to health experts and act now to reduce greenhouse gas emissions and protect the natural environment," the groups say.
Climate and Health Alliance executive director Fiona Armstrong said there can be no recovery with gas, the government's preferred measure to tackle emissions.
"The latest evidence suggests gas is just as emissions-intensive as coal," she said in a statement.
"Backing gas and fossil fuels will only accelerate the climate health emergency, further putting at risk the health of all Australians."
Public Health Association of Australia chief executive Terry Slevin said the impacts of COVID-19 had been severe and wide-reaching.
"Yet climate change is something which poses just as significant, if not a greater, challenge in terms of the impacts on human health, societies and economies," Mr Slevin said.
"We are already witnessing the public health impacts of climate change - through bushfires and smoke, through heatwaves, through communities devastated by drought."
Tackling climate change came back to the fore in the past week after US President-elect Joe Biden committed to returning his country to the Paris Agreement.