Temel Atacocugu (right) is consoled as he speaks at a memorial service for the anniversary of the March 15 attack, in which he was shot nine times. Photo / George Heard
The Christchurch gunman is the only individual on the list that's otherwise made up of international terror groups including Al-Shabaab, ISIL Sinai and the IRA.
It's up to Ardern to decide what individuals or groups should be classified as a terrorist or terrorist organisation.
She's given this power under the Terrorism Suppression Act which currently does not mention white supremacy or the far-right once.
Security analyst Paul Buchanan said Ardern should use that power as a preventative tool.
"By designating, let's say, a right wing extremist group ... as a terrorist entity, you cut them off from funding and make it illegal, for example, the [paying of] membership dues.
"Then if they're abusing the social media ... you can go after them for abusing the privilege of using the internet to communicate, that doesn't stop them from going to the clubhouse, dressing up and marching around.
"It certainly will make them think twice, if they choose to go on to public and harass and intimidate people in the way they used to before March 15," Buchanan said.
"But we don't need to wait until a member of a right wing group commits an act or an act of violence of any sword much less mass violence for them to be considered terrorists, or they are simply terrorists and name before the deed.
"And then as you know, people come down and keep their nasty views to themselves, you will have dissipated the threat without firing a shot."
The Government has to fulfil its promise to be proactive when responding to people with extremist views and recognise that white supremacists have "abrogated some of the rights and freedoms that the rest of us are protected by", Buchanan said.
Paul Spoonley, an expert on the far-right, is aware of many white supremacist groups here.
"I think there are probably somewhere around a dozen groups of various sorts who are active in this country. However, the number of individuals involved in those groups and involved in contributing to far-right discourse in this country has remained more or less the same and I would put that as somewhere between sort of two and 300," he said.
Spoonley was surprised by the list which he described as "traditional" and not reflecting the reality of the right-wing threat post March 15, 2019.
The legislation that covers the designation of terror entities (Terrorism Suppression Act 2002) was written in the wake of the 9/11 attacks and makes it difficult to classify white supremacists as a terror threat, Spoonley said.
"I think there is an appetite to identify these groups and the threat that they pose to our society and ... what's happening is our systems, including our definition of who is a terrorist, or what qualifies as a terrorist group is currently being updated.
"So I think that what we're seeing is a list which is historical in its origins and other definitions, and is inappropriate now and it needs to be expanded.
"So I am aware that there's quite a bit of work being done by various government departments, including the group that advises the Prime Minister on who should be on this list, to update and broaden and identify those groups in a way that's much more appropriate in the wake of the Christchurch shooting."
This would be in line with one of the royal commission into the Christchurch mosque attack's recommendations - which was for the government to review all counter-terrorism laws to ensure they were fit for purpose.
Minister of Justice Kris Faafoi wouldn't confirm officials were looking at changing the definition of terrorism.
But in a statement he said officials have started to look at the counter-terrorism laws, but work was in the early stages and it was too soon to say what changes may eventuate.
The royal commission found security agencies were too focused on the threat of Islamic extremism before March 15, 2019.
Islamic Women's Council national coordinator Aliya Danzeisen said the terror list showed nothing had changed.
"They clearly knew two years ago that there were concerns, they've done their own internal investigations, they have their own security ... and the fact that nothing's changed on these lists, other than adding the Christchurch shooter who was already caught and imprisoned, shows that their priority still remains or appears to remain elsewhere."
Danzeisen echoed Buchanan's comments, calling for the Government to take a proactive approach instead of a reactive one.