South Australia's attorney general says the state will continue to crack down on "imported hatred" after a number of alleged white supremacists were arrested at a January 26 rally in Adelaide.

On Sunday, SA police revealed 15 men and a youth from across the country were arrested and charged with various offences, including failing to cease loiter, possess articles of disguise, hinder and resist arrest—all of them National Socialist Network (NSN) members.

Two men - a 30-year-old and a 25-year-old from WA - were charged with the use of a Nazi symbol.

All the men were dressed in black and were arrested following a protest in front of a war memorial after a march through Adelaide's CBD.

At the Adelaide Magistrates Court court on Tuesday, prosecutors alleged 40 NSN members from across Australia assembled at the South Australian War Memorial.

"The National Socialist Network is a right-wing extremist group with national socialist ideology," the prosecutor said. "The group aims at preparing for a race war which it believes will usher in a white separatist ethno state."

Adelaide's 'Survival Day' rally was delayed to make sure the groups didn't cross paths.

Kyam Maher, the nation's first Indigenous attorney-general, said many people would see the behaviour as "akin to terrorism".

"I don't think any of us have any time for these sorts of people," he said.

One of the men charged, 30-year-old Mason James Robbins, appeared in court on Tuesday charged with carrying an offensive weapon or article of disguise and using a Nazi symbol.

Magistrate Luke David released Mr Robbins on a $600 bail, with strict conditions, including an exclusion from the Adelaide city area, a ban on wearing disguises in public, and a ban on associating with the 30 named people and members of the NSN and European Australian Movement.

He will return to court on March 11.

Asked about their attempt to "hijack" the "peaceful protest" on January 26, Mr Maher told reporters on Monday: "I think it says everything you need to know about the views these people hold."

"Just last year, laws came into effect that ban the use of Nazi symbols, or the Nazi salute people to face a $20,000 fine or a year in jail," he said.

"The sort of hatred and division we've seen imported from extremists from interstate should not be tolerated."

Prime Minister Anthony Albanese also condemned the behaviour of the neo-Nazis.

"They were horrific scenes yesterday, to have people openly identifying as neo-Nazis and fascists, white supremacists marching through our streets," he said.

"We cherish what overwhelmingly Australians have done, which is to come together, whether we can trace First Nations people back some 60,000 years or whether they are the newest migrants who yesterday took their oath of allegiance to Australia and became Australian citizens."

Mr Maher congratulated the police, arguing the people should take comfort in how quickly they were able to "understand what was going on and handle the matter".

"I think most South Australians are completely appalled at what we see from these right-wing groups," he said.

Footage showed the group of men singing Waltzing Matilda and "White Australia" chants, and it is understood one of the alleged people arrested was prominent white supremacist Thomas Sewell.

In video footage of his arrest, Mr Sewell can be heard yelling, "I am under arrest for celebrating Australia Day."

The prominent member of the National Socialist Network recently said he would "become a terrorist" and "start killing people" if child protection services began to remove children from neo-Nazi families.

Greens Senator Sarah Hanson-Young called for a full investigation into the state's "neo-Nazi cell".

She said the "Nazi invasion of Australia Day events is sickening" and argued attempting to scare or intimidate people was "completely unacceptable and must be dealt with by the full force of the law".

"Adelaide is a peaceful and respectful city, and we don't need Nazi-wannabes terrorising members of our community," Ms Hanson-Young said.

"These thugs don't embody the values of our city, state, or country. Racism, antisemitism, Islamophobia, and hate have no place on our streets or in our community."