Prime Minister Scott Morrison has welcomed the decision from sporting bodies to boycott hosting events in Russia following the country's invasion of Ukraine.
It comes as Australian aerial skier Danielle Scott said she would leave Russia and not take part in a world cup event that was due to be held in the country.
Scott, who recently competed at the Beijing Winter Olympics, said she could not believe the situation was happening.
"In the uniquely unifying power of sport, I wished so badly for this situation to be different," she said on social media.
As European football's governing body UEFA looks to strip St Petersburg of the hosting rights for the upcoming Champions League final, Mr Morrison said other sporting bodies should follow suit.
"The F1 should not be held in Russia, international tournaments should not be held there," he told reporters in Adelaide.
"I commend those Australians that are saying they won't participate in anything that is occurring in Russia this year ... this is how you impose a cost on Russia that is invading its neighbour."
The Russian grand prix is due to be held in the city of Sochi in late September.
Already, world champion driver Sebastian Vettel has called on the sport's governing body, the FIA, not to hold the event in Russia.
Vettel has already indicated he would boycott the race should it take place, calling it "wrong".
Mr Morrison said other sporting bodies should be making steps to cut off Russia in the wake of the invasion.
"We should be taking every step we can to ensure Russia pays a price in the international community for these violent and aggressive acts of invasion against Ukraine," he said.
