His comments came after 11 people were arrested for public order offences at an anti-lockdown protest in Dublin on Thursday.
Brief clashes took place on Grafton Street during which officers used batons and handcuffs after some protesters attempted to break a cordon set up in the area.
Mr Harris said the Garda response was “proportionate” because of the public order threat created by those involved.
He told a press conference on Friday: “These groups have shown a propensity to violence. We’ve seen in recent times, there has been violence at these protests.
“All of these matters are matters then which actually move it from the policing of Covid-19 restrictions, properly into public order legislation.
“In the end, last night we were using public order legislation to prevent what would have been a very frightening stampede up Grafton Street. That’s a tight enough pedestrian street and that can’t be allowed to happen either. ”
Mr Harris said the organisers of the protest are under active investigation, and that intelligence gathering has shown they are intent on unlawful behaviour.
He said: “Their intention is as stated through intelligence, we know they are there for an unlawful purpose.
“The disruption of legitimate business, the disruption of Government business or indeed the functioning of Government departments.”
Mr Harris said those involved were “a mix of groups with extremist views”.
He said a common characteristic of the groups is that they follow “the great replacement theory” which is linked with far-right extremists.
We've seen protests which have degenerated into violence, so it is appropriate then that we would have concerns.
Drew Harris, Garda Commissioner
Mr Harris said: “What we found concerning about these groups is you can see an initial call on open source media, then quickly they go to covert means of communicating with each other.
“That tells us right from the start there’s a problem here and we should be concerned about the protest activity that’s going to follow.”
He added: “Once we become aware of protests being organised, we do try to find out intelligence about it, because we have a concern about the risk of violence.
“We’ve seen protests which have degenerated into violence, so it is appropriate then that we would have concerns.
“These protests, they are covert at a certain point. Their arrangements do become covert, and we do seek then intelligence in respect of that.”
Mr Harris acknowledged that the pandemic had become a recruitment ground for these type of groups.
He said: “Certainly if you take this on an international basis, it has been one of the drivers around some of these extreme groups and the views that they express. I think less so here in Ireland, but it has had some impact.
“But we haven’t seen in effect the increase in such behaviour that’s happened elsewhere, particularly on the continent of Europe. So we should be pleased about that.
“The great majority of people want nothing whatsoever to do with this. You’re only talking about small numbers of individuals and we then have responsibility to police those protests.”
He also expressed concern that footage taken from the protests could be edited and used as a means of propaganda for the groups.
He said: “There is always a threat around these groups, be it far left or far right, using footage and then using them as propaganda.
“We are there for a legitimate purpose. We responded appropriately to what we could see as a threat that group was posing in terms of public order.”
One of the difficulties in policing the protests, Mr Harris said, is that organisers are refusing to come forward, meaning gardai have no one to negotiate with.
He added: “I hope those who organise these protests realise that they’re under focus, that we’ve engaged in active investigation.
“The description of what an organiser (is) has been expanded, and we’re mounting investigations to identify those individuals and then report them to the director of public prosecutions as well. “