The PSNI says some anti-racism rallies planned for Saturday have been called off after it held talks with the organisers.
The protests were arranged in response to the death of African-American George Floyd in US police custody.
The police say large gatherings during the pandemic pose a public health risk and are not allowed.
The demonstrations that were due to take place in Omagh, Portadown and Newry will not now go ahead.
Rallies have also been organised in Belfast and Londonderry.
Large crowds gathered at Belfast City Hall on Wednesday to protest at the death of Mr Floyd.
First Minister Arlene Foster has warned against further demonstrations due to the risk to public health.
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.
PSNI Assistant Chief Constable Alan Todd has welcomed the cancellation of some demonstrations after he warned that those who attend "are likely breaking the law in travelling to events" and also by attending "any gathering of six or more people".
"We are engaging with, explaining to and encouraging organisers to cancel and potential protesters not to go to these events," he said.
"However, if this advice - which comes from health professionals, elected representatives and the chief medical officer as well as police - is ignored and people break the law, then there will be consequences."
He said those who do attend protests may be fined or end up in court.
"This weekend, there will be a more visible police presence at the events themselves, as well as at bus and train stations and on the roads," he said.
"In normal circumstances, we would work with organisers to facilitate peaceful protests - but these are not ordinary times.
"Protesting against the unnecessary and unjustifiable death of a person in the United States risks the unnecessary and unjustifiable deaths of people in Northern Ireland who could contract the virus as a result."
Mrs Foster asked people to "find different ways to protest".
Speaking to BBC Radio Ulster's Good Morning Ulster programme, she said the law "is clear on mass gatherings" during the pandemic.
She said people have "cancelled mass gatherings because it's against the law", and referred to funerals and the cancelled Twelfth of July celebrations.
The PSNI estimated that between 1,500 and 2,000 people attended the rally in Belfast.
"It will be a couple of weeks before we see the impact of that mass gathering in Belfast the other day; we will see if it has had an impact on the virus", Mrs Foster said.
Leaving your house to protest at the weekend is putting your health and the health of others at risk. As a society we are fighting a global pandemic. Mass gatherings will push back the progress we have made. Please follow the @niexecutive #COVID19 regulations. #StaySafeSaveLives pic.twitter.com/67lDZchswV— Police Service NI (@PoliceServiceNI) June 5, 2020
NI's Chief Medical Officer Michael McBride said there was "no cause that this virus respects".
He said the right to protest must be balanced against the need to control the spread of the virus.
"Think of alternative ways to express your outrage," he said.
George Floyd, 46, an African-American man, died after being arrested by police outside a shop in Minneapolis, Minnesota.
Footage of the arrest on 25 May 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.
The protests have spread to the UK and Republic of Ireland.
Jolene Francis, who helped organise the Belfast rally, told the BBC she wanted to send a message of solidarity to "our friends over in America".
She said while social distancing was important, she believed there was a "social responsibility to show our solidarity and demand justice against racial discrimination".
A Londonderry mother whose African-American son was born in New York says she would fear for his safety if he ever returned to the United States.
Maria Morris has a 20-year-old-son, Isaiah.
"Would I fear him going to the US on his own? Yes, I think I would do everything in my power to stop it," Mrs Morris told BBC Radio Foyle.
"He is now afraid as a young, black male to ever go back to the country of his birth."
Lillian Seenoi-Barr, director of programmes at the North West Migrant Forum, said she felt the death of George Floyd "deep in her stomach".
Mrs Seenoi-Barr, who has family in America, said she now "fears the worst" every time she receives a phone call from them.
"Watching George's life being taken on camera has been horrific, his voice has not come out of my head," Ms Seenoi-Barr said.