Gardai will seek advice from the DPP over protests held under the Black Lives Matter banner over possible breaches of the Covid-19 restrictions governing social-distancing and travel.
A garda spokesman said the force has been in contact with protest organisers to make them aware of their obliga- tions under coronavirus regulations.
One peaceful protest, in the aftermath of the killing of George Floyd in Minneapolis, took place at the US embassy in Ballsbridge on Saturday and was attended by a large number of demonstrators.
Gardai advised organisers of the health risk to participants and the wider community from such gatherings.
The spokesman said the Health Act put in place to help curb the pandemic set out lim-its on the movement of people.
"Such measures have been put in place to help stop the spread of the Covid-19 virus," he said.
"In addition, both the Chief Medical Officer and the Minister for Health have stated that such mass gatherings should not take place as they may pose a health risk to those taking part and those that attendees have contact with after the event."
A garda statement said: "In supporting the Covid-19 public health guidelines and regulations, An Garda Siochana has, and will continue to, adopt a graduated policing response based on its tradition of policing by consent.
"This has seen members of An Garda Siochana engage, educate, encourage and, as a last resort, enforce.
"In line with this, organisers of protests are being advised by gardai that such protests may constitute a potential breach of the regulations.
"As with all potential breaches of the regulations, investigating gardai must seek the advice of the Director of Public Prosecutions in respect of any further actions to be taken.
"The Covid-19 pandemic remains a public health crisis, and An Garda Siochana continues to appeal to all citizens to comply with public health guidelines and regulations, in particular essential journeys, in order to continue to save lives."
There were no arrests at Saturday's protest, which was organised by Black Pride Ireland, MERJ (Migrants and Ethnic Minorities for Reproductive Justice) and MASI (Movement of Asylum-Seekers For Ireland).
The demonstration passed off peacefully.
A rally held last Monday was criticised for participants not conforming to social-distancing rules, and gardai said they were investigating possible breaches of public health guidelines and regulations.
A similar protest that was due to be held today has been cancelled.
In a statement, organisers said a number of safety concerns and potential criminal offences surrounding the protest were raised, and they decided to cancel today's demonstration, with the possibility of rescheduling.