Three American troops have been killed in the conflict, the Pentagon confirmed.
Defence Minister Richard Marles said US facilities in Australia were not used in the attack, describing Iran's leadership as "abhorrent".
"We do support the action that the United States has taken, and we very much stand with the Iranian people in this moment," he told ABC radio on Monday.
Asked if the attacks were deemed legal under international law, Mr Marles replied: "Ultimately, the legality of these measures is a matter for both the United States and Israel to go through."
Australia-based human rights advocate and lawyer Sara Rafiee called for continued international pressure to help dismantle the regime's coercive practices, security infrastructure and command centres.
"Iranians are unequivocal in one thing: reform within the current system is not an option," she said.
"After 47 years of repression, they want the regime gone in its entirety and the opportunity to determine their own future."
Iranians in Australia took to the streets to celebrate the strikes on Tehran, marking them as the beginning of the end for the brutal regime.
Rallies took place in Sydney, Melbourne and outside the former Iranian embassy in Canberra, where members of the community sprayed champagne, cheered and danced.
A jubilant Nadeo Ranjear welcomed the Ayatollah's death as "the greatest, greatest news".
"It is still the beginning of the end. We still haven't got 100 per cent victory, but we are almost there," he told AAP outside the embassy on Sunday.
"Victory is around the corner ... the Iranian people will overthrow this regime."
Some smaller, anti-war demonstrations also broke out, with groups such as the Jewish Council of Australia condemning Prime Minister Anthony Albanese's endorsement of the US strikes.
Australian Travel Industry Association chief executive Dean Long warned travellers transiting through the Gulf to expect delays and rerouting "for the foreseeable future".
He warned Australians not to cancel flights, even to nations upgraded to do-not-travel warnings.
"Let the airline or tour operator make that call - if they cannot provide the service because it is unsafe, your rights are much better protected," Mr Long said.
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