The cabinet's National Security Committee is due to receive an urgent briefing from ASIO and the AFP on the risk posed by right-wing extremists following the terror attacks on two New Zealand mosques.

ASIO director general Duncan Lewis and Australian Federal Police Commissioner Andrew Colvin will brief Prime Minister Scott Morrison, who chairs the committee, and its members on Monday.

Australian white supremacist Brenton Tarrant allegedly stormed the Christchurch mosques, during Friday prayers and shot dead 50 Muslims and wounded dozens.

As announced yesterday, our Government will lead a bipartisan motion in the Parliament to denounce these terrorist acts of hate, and those who make excuses for it. https://t.co/VIFxQc3ZPX — Scott Morrison (@ScottMorrisonMP) March 17, 2019

Nick Kaldas, a former NSW Police deputy commissioner and now a senior fellow at the Australian Strategic Policy Institute, said the growth of right-wing extremists had not been adequately monitored.

"It has been clear for some years that there is a lot of activity in the right-wing group space,'' Mr Kaldas told The Australian.

"It's incumbent on authorities now that the threat has become so visible that they change tack and dedicate more resources to monitoring that type of group.''

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It comes as Victorian Police revealed dozens of right wing extremists are on terror watch lists, and monitoring of the so-called alt-right has escalated after the deadly attack in New Zealand by an Australian.

Chief Commissioner Graham Ashton on Sunday said police were keeping tabs on the Victorian extremists, particularly online.

"After Friday we have intensified our monitoring of the alt-right individuals within Victoria," Mr Ashton said.

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"We've been monitoring also a range of individuals since Friday, we're just making sure we're not seeing any increased levels of anxiety around any sort of action and certainly to date we haven't seen that."

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Mr Ashton said he spoke with his federal counterpart about monitoring online rhetoric that might constitute a federal offence.

"These threats can emerge very quickly and often from very little information or intelligence beforehand," he said.

"You do the best you can, we make sure we're plugged into what's happening in the intelligence arena, particularly with our federal partners."

Organizers of an Open Day at the Australian Islamic Centre in Newport, Victoria say they are touched and heartened by the support of local people after the #NewZealandTerroristAttack Cards and flowers are being brought by visitors. @SBSNews pic.twitter.com/1ZPz1Sjhv1 — PhillippaCarisbrooke (@PCarisbrooke) March 17, 2019

People of all races and faiths are visiting Victorian mosques as part of an Open Day intended to build cross-cultural understanding. Organisers say the event has extra meaning after the #NewZealandTerroristAttack @SBSNews pic.twitter.com/rABjfF8fU8 — PhillippaCarisbrooke (@PCarisbrooke) March 17, 2019

Mr Ashton was at Preston Mosque on Sunday alongside Premier Daniel Andrews as part of a pre-organised, statewide open mosque day.

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Anti-immigration white nationalists violently leapt on a teenager who egged Queensland Senator Fraser Anning at an event in suburban Melbourne on Saturday.

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Among them was convicted criminal Neil Erikson who is currently going through the courts again.

Mr Ashton said he's directed his officers to go through footage of the incident in its entirety to consider whether assault charges and breach of bail offences might also come into play.