Chief Constable Simon Byrne will be handing a report to the Policing Board to explain why fines were issued to people during the Black Lives Matters protests and not the 'protect our statues' demonstrations.
The PSNI issued 68 fines to people breaking social distancing regulations at the anti-racism protests in Belfast and Londonderry earlier this month.
However, no fines were given to those who took part in the right-wing demonstration outside Belfast City Hall on Saturday.
Referring to the policing approach during yesterday's Covid-19 briefing, First Minister Arlene Foster said she had discussed the issue with Mr Byrne during a prearranged meeting.
She said that it was important to be consistent in the "application of law" and confirmed that the Chief Constable would be giving a report to the Policing Board on the operational issues.
"I think it is a matter for the Policing Board to raise with the Chief Constable," the DUP leader said.
"It is so very important and I know there has been a number of groups that have come together and we understand that people want to congregate together for different reasons, sometimes for social reasons and sometimes for issues of protest, but people need to remember that the regulations are still in place in terms of mass gathering."
Deputy First Minister Michelle O'Neill added the police must be consistent when enforcing the Covid-19 regulations.
"I know my party colleague Gerry Kelly has also raised this at the Policing Board, but these are operational matters for the PSNI," she said.
"I haven't spoken to the Chief Constable directly on this.
"I'm quite sure I'll have an opportunity to do so, but I know the Policing Board are looking at this.
"You need to be consistent in anything you do, so I think it's also important that the police are consistent."
Yesterday Boris Johnson defended his decision to launch a commission on racial inequality after Labour claimed it was a "back of a fag packet" plan designed to "assuage the Black Lives Matter protest".
The Prime Minister said the Commission on Race and Ethnic Disparities would learn "very fast" what changes needed to be made.
But shadow justice secretary David Lammy said there have been several reviews into racism in the UK in recent years.
Mr Johnson, who also faced criticism for saying he wanted to "stop the sense of victimisation and discrimination", acknowledged that racism "unquestionably" existed in the UK.
He told reporters in Downing Street: "The whole point of having a review is to look at the areas where people feel there's more that needs to be done. I think what we want to do is learn now very fast what fresh changes we need to make.
"What I feel most strongly is that there are so many positive stories that are not being heard.
"Things really are changing. You're seeing young black kids now doing better in some of the most difficult subjects in school than they were ever before, more going to top universities.
"We need to start telling that story and building up a culture of high expectations, a narrative about success, as well as stamping out the racism and the discrimination that unquestionably exists."
Mr Lammy criticised the Government for not providing details on the scope of the commission, which was launched in a Daily Telegraph article by the Prime Minister. Also yesterday Home Secretary Priti Patel took a swipe at Labour leader Sir Keir Starmer. Ms Patel accused Sir Keir of not deviating from the "divisive, hateful, racist politics of its former leader" Jeremy Corbyn in refusing to call out "racist and intolerant behaviour" from people on all sides of the political spectrum in recent weeks.
She also condemned a letter she received from Labour black and minority ethnic MPs accusing her of "gaslighting" black people's experience of racism as "pathetic".