The Sonnenkrieg Division, a neo-Nazi group active in the United Kingdom, was listed on the government's register of terrorist groups in March, marking the first time an organisation with extremist right-wing views had been added.

But a government submission has shown its ties to Australia are minimal and statements made by the group have never threatened Australians or their interests.

It comes as a Business Insider Australia report on Wednesday revealed two South Australian men had been arrested for allegedly being in possession of an improvised explosive device and extremist material. The men have reported ties to a known Australian neo-Nazi group not listed on the terrorist register.

In the submission to an inquiry examining Sonnenkrieg's listing, former home affairs minister Peter Dutton said Australians were not "directly involved" with the group but the material it distributed could contribute to radicalisation and inspire lone wolf attack.

"[Sonnenkrieg Division] has not made statements specifically threatening Australians or Australian interests, but adheres to an ideology that is violently opposed to multi-ethnic Western societies," the submission read.

"The UK has a high population of Australians, and Australians have been killed and injured in previous terrorist attacks in the UK.

"There is a possibility that a lone-actor attack directed or inspired by SKD could result in harm to Australians."

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Mr Dutton announced his intentions to list the group in early March, noting he was particularly concerned about its reach in the country.

Labor's Home Affairs spokesperson Senator Kristina Keneally said at the time other violent groups needed to be considered, too.

"Australia is the last of the Five Eyes countries to designate a right-wing extremist group as a terrorist organisation," she said.

"There are several other right-wing extremist groups, some with direct links to Australian groups, that have already been proscribed by our Five Eyes partners.

"The question for the Morrison government now is whether those other groups will also be proscribed in Australia."

Head of Australia's domestic spy agency Mike Burgess told a parliamentary committee in March it had put forward other groups for inclusion on the register.

"There are other groups we have proposed. How that happens and whether or not they meet the legal threshold is a matter for others," Mr Burgess said.

"[Sonnenkrieg is] not highly active, but it does have residents here."

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