Thousands marched on the weekend to protest Israel's mass killing of civilians in Gaza and bombing of Lebanon but some have been condemned for carrying the Hezbollah flag and photos of its killed leader.
Jewish Australians have called out the use of the listed terror group's iconography and photos glorifying Hassan Nasrallah.
Protesters were joined by some who brandished the Hezbollah flag and photos of its slain leader. (James Ross/AAP PHOTOS)
Executive Council of Australian Jewry co-leader Alex Ryvchin called it "sickening to see fellow Australians on our streets mourning the death of this terrorist kingpin".
The protests went beyond concerns about the loss of life and future of Lebanon and veered into "active, open, specific support for Hezbollah" which police needed to take action against, Mr Ryvchin said on Monday.
The Islamic Council of Victoria blamed a small number of people for the Hezbollah flags, saying the community's focus was on the escalation of violence in Gaza and Lebanon.
"It has been made clear that Hezbollah flags are not welcome and should not be brought," the group's president Adel Salman said.
Jewish leaders say it was "sickening" to see people openly mourning the death of a terrorist leader. (James Ross/AAP PHOTOS)
However fixating on flags served as a "convenient distraction" from violence in the Middle East, Australia Palestine Advocacy Network president Nasser Mashni said.
"It's a national disgrace that condemning a flag has become easier than confronting the brutal reality of a rogue state intent on annihilating an entire population."
Foreign Minister Penny Wong has warned Lebanon "cannot become the next Gaza" and supported a 21-day ceasefire proposal.
Political leaders have also expressed concern over the flames of social conflict being fanned by protest actions.
The prime minister says radical ideologies aren't welcome in Australia. (James Ross/AAP PHOTOS)
"We do not want people to bring radical ideologies and conflict here, our multiculturalism and social cohesion cannot be taken for granted," Prime Minister Anthony Albanese said ahead of a cabinet meeting in Canberra on Monday.
Home Affairs Minister Tony Burke warned visa holders and applicants who sought "to incite discord in Australia" could have visas refused or revoked.
A spokesperson for Attorney-General Mark Dreyfus said legislation last year created serious criminal offences for the public display and trade of symbols used by terrorist organisations.
"The new laws also ensure that glorifying and praising acts of terrorism are criminal offences under commonwealth law," he said.
Mr Dreyfus said the AFP had confirmed they were investigating a number of breaches, believed to be as many as six.
But "the mere public display of a prohibited symbol on its own" doesn't reach the commonwealth law threshold, an AFP spokesperson said.
The symbol needed to be used in actions that spread ideas of racial superiority or hatred or were likely to offend, insult or intimidate a person for reasons such as race, religion or nationality before anyone could be charged.
Officers can direct people to take down the symbols but can't remove them by force, although those who fail to comply face fines.
Hezbollah flags were confiscated by police when protesters failed to put them away for good. (James Ross/AAP PHOTOS)
In NSW, protesters initially complied when asked to put away Hezbollah flags but many brought them out later, prompting police to seize at least two flags.
Parliament should be recalled to urgently pass legislation criminalising the glorification of a terrorist leader if current laws weren't strong enough, Opposition Leader Peter Dutton said.
Coalition frontbenchers are further demanding visa cancellations for anyone supporting Hezbollah.
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