Australian Security Intelligence Organisation Director-General Mike Burgess fronted Senate estimates on Monday afternoon to answer questions on the rising threat of ideologically motivated violent extremism, formerly referred to by the agency as right-wing extremism.

Mr Burgess has repeatedly warned the threat has continued to increase in recent years, with it now taking up between 30 and 40 per cent of the organisation's priority caseload.

An Australian man, motivated by far-right ideologies, was convicted of murdering 51 people in a Christchurch mosque in 2019 but ASIO has said it collected no information on him that could have prevented the attack.

Greens senator Mehreen Faruqi asked Mr Burgess about comments he made days earlier on why he believed there were no direct lessons for ASIO to learn from the incident.

"The person was in contact with Australian far-right groups, lived in Australia, was an Australian man. How are there no direct lessons for Australia here?" Senator Faruqi asked on Monday afternoon.

Mr Burgess defended his comments, pointing to the limitations the agency had in monitoring all of society.

"We do not live in a surveillance state and ASIO is not all-seeing and all-knowing," Mr Burgess said.

"If an individual in this country is in contact with others in other countries, or even in this country, and doing things, which are abhorrent to all of us, you cannot expect us to [provide] 100 per cent assurance."

He added legislation constrained the domestic intelligence agency from identifying every threat but it was part of the design.

"We work really hard to identify these threats but there is the law that enables what we do and the law that binds and bounds what we do," Mr Burgess said.

"So if you're suggesting we should have some form of all-seeing or all-knowing apparatus, I would respectfully disagree."

Mr Burgess told Guardian Australia the shocking attack was a reminder these attacks could occur and the agency was continuing to focus on these situations.

He later clarified there were no lessons as the offender had left Australia as a young man, limiting the intelligence that could be gathered.

A New Zealand royal commission report last year found evidence showing the convicted offender had been involved with Australian far-right groups.

He was allegedly reported to Australian authorities for threatening behaviour but managed to avoid being on the organisation's radar.

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Earlier on Monday, it was announced right-wing extremist group Sonnenkrieg Division had officially been added to the country's terrorist listing.

Members of the group have been convicted for plotting to attack the British royal family, as well as disseminating terrorist material.

The group marked the first politically-motivated extremist group to be added to the list, joining 25 other terrorist organisations.

The listing enables all available terrorist offences and penalties to apply to the organisation, including up to 25 years in jail for some offences.

Mr Burgess was asked by Labor senator Kristina Keneally on Monday afternoon whether the intelligence organisation had recommended other far-right groups be added to the list, following moves by other Five Eyes countries.

Mr Burgess said it had proposed other groups but it was up to others in government to decide if the legal threshold was met.

"Here it's a very high bar because there are very high penalties," he said.

"Of course we will pay attention to any groups here in Australia and we look at them but our principal focus is actually on individuals and the group itself about whether they promote acts of violence or terrorism."

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