The Victorian government said it was open to looking at further action against the display of hate symbols after a group of protesters performed Nazi salutes outside parliament on Saturday.
WARNING: This story contains images some readers may find distressing.
Clashes broke out on Saturday between rival protest groups on the steps of Victoria's parliament after a group of men performed Nazi salutes.
The men had gathered in support of British anti-transgender activist Posie Parker, also known as Kellie-Jay Keen-Minshull, who was speaking at the demonstration as part of a national tour.
A number of groups converged on Parliament House, including supporters of Ms Parker, people displaying anti-vaccine slogans, and a large counter-rally in support of trans rights.
One group of men, many masked and dressed in black, performed the salute several times while being separated by police from a group of counter-protesters.
Last year, Victoria became the first jurisdiction in Australia to ban the Nazi swastika, with those who defied the ban facing jail terms and hefty fines.
The legislation did not include the Nazi salute, also known as the Sieg Heil.
Federal Labor MP Josh Burns called for the salute to be banned.
"It makes no sense that it's now illegal to display a Nazi symbol in Victoria, which is fundamentally a good thing, but you are allowed to do what happened yesterday which is walk up and down Spring Street doing the Sieg Heil and saluting neo-Nazi ideology," he said.
"I think we need to look across government about what laws are required across the country, how we can work with and between different layers of government in order to ensure that this sort of bigoted and really ugly scenes we saw don't happen again."
Mr Burns said "history shows that we need to be very careful and call out this behaviour".
"When my grandmother left Germany, they made the Jewish people wear a yellow star, and they made the LGBTIQ community wear a pink triangle," he said.
Victorian Premier Daniel Andrews condemned the actions of the demonstrators on Twitter, saying Nazis were not welcome in Victoria and trans rights were not negotiable.
Deputy Premier Jacinta Allan described the salute by the demonstrators as "disgraceful" and said it had no place in Victoria.
"What we saw in the CBD yesterday were a bunch of cowards acting in a cowardly and disgraceful way with the sole purpose to try and intimidate people going about their business in the centre of Melbourne," she said.
"The Attorney [General] and the minister will be looking at what further action could be taken to address this sort of behaviour."
Multicultural Affairs Minister Colin Brooks said the government would not rush in to ban the salute but would consider whether such a move would be effective.
"We want to do what we can to eradicate that ideology, that ideology of hate, and banning symbols and gestures is an important move."
Anti-Defamation Commission says state needs to 'send a very clear message'
Chair of the Anti-Defamation Commission, Dvir Abramovich, said he welcomed the commitment from the government to investigate strengthening the laws.
Dr Abramovich, who was a key proponent of outlawing the display of Nazi symbols, said the state needed to "send a very clear message that neo-Nazism will never find a refuge and safe haven in Victoria".
"For a Holocaust survivor, seeing this Nazism is as frightening as being threatened with a gun," he said.
Opposition spokesman David Southwick said his party would work with the government to ensure police had the power and resources to prevent a repeat of the episode.
"This is a blight on Victoria when we've got a situation where we've got Nazis standing and effectively Nazi saluting on the steps of Parliament House. It's really unacceptable for that to happen," he said.
Speaking at a Jewish community event on Sunday, Mr Southwick was questioned about the attendance of Liberal upper house member Moira Deeming at the Posie Parker "Let Women Speak" portion of the crowd.
Mr Southwick said of Ms Deeming: "Her views are not my views, and I don't think the views of the Liberal Party and most of mainstream Victoria.
"But she has a right to her views, and at the end of the day, it is one thing about expressing those views and expressing them peacefully, but those neo-Nazis are the focus for me. And that's where the laws need to be there to ensure that those people don't behave that way."
Ms Deeming said she was "disappointed with Victoria Police", who she said, "somehow could only walk masked men past us they did a horrible Nazi salute".
Many of the crowd who were there to support trans rights expressed disappointment and anger on social media at the role of police, who were seen holding the counter-protesters back while allowing the saluting men to walk past Parliament House.
Police association Secretary Wayne Gatt said police officers would have been "disgusted" at the actions of the men performing the salute, but were required to protect them from counter-protesters.
"I think it would've gone against every human instinct that we have as police, and that is that sometimes we have to protect people that we very much disagree with," he told radio station 3AW.
"What we see those groups represent is nothing but pure racism and I'm not sure that it has any place in our streets or in our community."
Mr Gatt said he was not sure banning the Nazi salute would be effective.
"People who are hell-bent and intent on causing offence and outrage will just find something else. They'll find something else to do to replace the thing that was outlawed."
Victoria Police said officers arrested three people during the protests, which a spokesperson said involved at least six distinct groups.
