It follows two arrests on Saturday when violence broke out between opposing sets of protesters during anti-mask demonstrations outside Leinster House.
Assistant Commissioner for Policing and Community, Paula Hilman said that while there is a balance to be struck between the right to protest and public health, those committing offences will be investigated.
Asked about Sunday’s protest, she said: “Throughout the Covid-19 pandemic, we have applied a proportionate response to that.
“In doing so, we firstly engage with people, we explain, we encourage and then the fourth tier is to enforce.
“Now, we have a role as a police service to then enforce the law and we will police the protests and at the outset engage with the organisers. But where potential offences have been committed, then we will look at investigating those offences.”
She said there is no “easy solution” to the anti-mask protests, which have seen hundreds of people participating in large gatherings in Dublin and across the country.
“There is a right to peaceful and lawful protest but that also in today’s environment has to be balanced with health, with what we’re dealing with in a pandemic. So it is a balance.
“There’s not an easy solution. But we will play our part in both engaging with organisers and having any proportionate policing response to what is required and the situation that we face."
Ms Hilman was speaking today at the Mansion House in Dublin, where Gardaí and local authorities issued an open letter to citizens of the capital to adhere to public health guidelines.
She added: “I would encourage everyone to work together. What today is about is everyone playing their part in keeping our society safe, to comply with what we need to do, to stop the spread of the pandemic.
“That’s by maintaining social distancing, wearing a mask, limiting contacts.”
The open letter called on Dubliners to take responsibility for their actions and work together to reduce the spread of the coronavirus.
It was signed by Dublin lord mayor Hazel Chu, Dun Laoghaire-Rathdown Cathaoirleach councillor Una Power, Fingal mayor David Healy and South Dublin mayor Ed O’Brien as well as Dr Deirdre Mulholland of the HSE, and Ms Hilman.
Our four Dublin Mayors have come together with An Garda Siochana & the HSE to sign an open letter to the citizens of Dublin to encourage us all in our fight against #COVID19.
The Open Letter calls on Dubliners to take personal responsibility for their actions #HoldFirmDublin pic.twitter.com/74BfOjeYLR— Dublin City Council (@DubCityCouncil) October 12, 2020
Speaking afterwards, Ms Chu said that there is a “tiredness” setting in with regards to the pandemic restrictions, but urged people to keep up the fight and protect each other.
She said: “I think there’s a tiredness that’s setting in. I’ve heard words like complacency, lethargy, but I think exhaustion is really the right thing to note it as. Because that’s what people are, people are tired.
“The thing is, the CMO (Dr Tony Holohan) is reiterating it not because he thinks people aren’t adhering to it. It’s because he knows that if he keeps saying it, people will continue to fight. That’s what we need to do.
She added: “Those numbers that we see every day. Those are real live numbers with lives that are lost. We need to see those as people that we can protect.
“This is something that we can all do, which is bound together and make sure that we continue to adhere to restrictions.”