Kristina Keneally, Labor's Home Affairs spokesperson, on Thursday evening called for a national discussion about how widespread far-right extremism has become, reports Xinhua news agency.
The Opposition has said that Australia was the odd one out among the Five Eyes intelligence alliance, which comprises Australia, the US, the UK, New Zealand and Canada, in not officially listing any right-wing groups as terrorists.
"Such proscription would be symbolic, but it would be more than just symbolic," Keneally said in a speech to the Australian Strategic Policy Institute, according to the Australian Broadcasting Corporation.
Some experts suggest that, in our increasingly networked world, any practical distinction between domestic and international terrorism has almost gone completely.
"Movements do not exist in isolation, but rather link and take inspiration from each other and from individuals within movements," she added.
Officially listing an organization or individual as a terrorist in Australia gives authorities extra powers to monitor them.
She said that potentially dangerous ideologies had spread quickly online during the Covid-19 lockdown.
"Right-wing extremists are hiding in plain sight, on Facebook and other common-use social media platforms.
"They use certain words and phrases that have everyday meanings but also convey coded content to those in the know."
Keneally's comments came after Australian national Brenton Tarrant was sentenced to life imprisonment without parole for carrying out the 2019 Christchurch mosque shooting, which calimed the lives of 51 people.
On September 1, the New Zealand government designated Tarrant as a terrorist entity.