Hundreds of people joined the anti-racism rallies at Custom House Square in Belfast and the Guildhall in Londonderry in response to the death of George Floyd in US police custody.
The PSNI conducted checks on roads and at transport hubs ahead of the protests.
As people arrived in Belfast, many wearing face coverings and gloves, at the demonstration in Belfast they were handed flyers by police officers detailing social-distancing rules. Some were issued with community resolution notices.
Organisers had marked out social-distancing measurements and encouraged those attending to space out.
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They heard speeches and at one stage knelt on one knee in solidarity.
Assistant Chief Constable Alan Todd said: “There were five events in support of ‘Black Lives Matter’ planned to take place at locations in Belfast, Derry/Londonderry, Omagh, Newry and Portadown yesterday and today.
“Three of these events – in Omagh, Newry and Portadown - were cancelled however the events in Belfast and Derry/Londonderry proceeded, contrary to the current Health Protection Regulations.
“Despite the cancellation of the Newry event, a small crowd did gather but dispersed quickly on our request.
“We conducted checks on travel routes and transport hubs across Northern Ireland today, requiring people to return home rather than travel to the unlawful protest gatherings.
“I believe that these actions had a positive effect on reducing the number of people attending the protests thereby protecting the public from the spread of the coronavirus.
“We estimate there were less than 500 people in attendance at each event and a significant number of Community Resolution Notices (CRNS) and fines were issued in both Belfast and Derry/Londonderry.
“A number of individuals, including organisers, will now be reported to the Public Prosecution Service with a view to prosecution. We will also conduct follow up enquiries to seek to identify others who may have committed offences.
“As I have said previously, in other times, we would have been working with the organisers and protestors to facilitate a lawful and peaceful protest to mark the avoidable and unnecessary death of George Floyd, however, these are not ordinary times.
“The Health Protection Regulations are in place to protect us all during this pandemic and it is everyone’s responsibility to adhere to them to protect our society.”
Patrick Corrigan, Amnesty International’s Northern Ireland Programme Director, said reports of fines being imposed on demonstrators are “deeply worrying”.
He added: “People have taken to our city’s largest public squares to express their rage at the murder of George Floyd, and take a stand against the racism which BAME people experience in the US and closer to home. Their voices must not be silenced.
“I pay tribute to today’s protest organisers in Belfast and Derry-Londonderry, who went to great lengths to ensure protests were socially distanced and safe for participants in light of the current public health crisis.
“The PSNI must respect the rights of those peacefully protesting and ensure that the voices of those demanding action on tackling racial injustice are allowed to be heard.”
Parliament Buildings will be lit up in yellow on Saturday as a sign of solidarity with the Black Lives Matter movement.
The Assembly Commission said the gesture was “a strong and visible symbol” of opposition to racism.
George Floyd, 46, died after being arrested by police outside a shop in Minneapolis, Minnesota.
Footage of the arrest on May 25 shows a white police officer kneeling on Mr Floyd’s neck while he was pinned to the ground.
Derek Chauvin, 44, has since been charged with second-degree murder.
His death has led to widespread demonstrations and civil unrest in the US and further afield.