Iran's state media criticised the team for refusing to sing the Iranian national anthem before their first match of the Asian Cup in Australia, calling them "wartime traitors" who must be dealt with severely.
Community groups have written to Home Affairs Minister Tony Burke, pleading with him to intervene on behalf the women.
The team is staying at the Royal Pines resort on the Gold Coast and is due to leave Australia later this week after completing their Asian Cup matches.
Rana Dadpour, the founder of women's rights group AUSIRAN, said government officials should organise private meetings with the team members before they leave the country, warning they could face execution if they return home.
"We need to talk with these girls away from the handlers and the regime-affiliated people who are following them right now in Australia," she told AAP.
"If they want to stay, I think we need to provide them with every support that we can."
While government officials have been reluctant to discuss the team's plight, fearing the publicity could put the women and their families at further risk, Ms Dadpour said global pressure was often effective on the Iranian regime.
"We've had many cases of execution orders that have been previously delayed or stopped only because of the international pressure and media attention," she said.
Leaving their final match of the competition on Sunday night, at least one of the women appeared to make the international signal for help through the window of the team bus - raising an open palm, crossing the thumb over it and folding the four fingers over the top.
Protesters surrounded the bus and the women appeared to film the crowd through the window.
Reza Pahlavi, the son of Iran's former Shah and a leader of the nation's resistance movement, said the decision not to sing the anthem was a brave act of disobedience, but meant the team would face "dire consequences" if they were to return to their home country.
"I call on the Australian government to ensure their safety and give them any and all needed support," he said.
Opposition frontbencher Julian Leeser has urged Australia to grant the women asylum if they want it.
"The Australian government should not turn a blind eye to the danger these women face," he said in a statement.
The government is highly sensitive to speculation about the women's potential movements, fearing it could further imperil them should they return home, or put their families at risk.
Attorney-General Michelle Rowland said she recognised the women's bravery but wouldn't be drawn on whether Australia had approached them to offer asylum.
A change.org petition calling for Australia to intervene in the women's plight had garnered nearly 60,000 signatures as of Monday morning.
