Arlene Foster has said mass gatherings during the pandemic such as the one in Belfast in the wake of the killing of George Floyd in the US "are dangerous, however laudable the cause may be".
Speaking at the daily Executive Press briefing, the First Minister said Wednesday's gathering of over 1,000 people at the City Hall in support of the Black Lives Matter campaign was in clear breach of regulations.
"We need to be careful that in our enthusiasm to restore the rights we previously had we exercise them responsibly and don't lose our sense of perspective," she said.
"Covid-19 is still claiming lives and it can do that when crowds gather, even in dozens, and social distancing is ignored.
"Many have cancelled mass gatherings for very good reasons. People have been denied the chance to attend the funerals of family and friends. Mass gatherings such as we saw yesterday are dangerous, however laudable the cause may be."
The PSNI is not taking any action over the protest rally, but Mrs Foster said police would be keeping a close eye on any further breaches.
Deputy First Minister Michelle O'Neill warned that people must act responsibly.
"The world has watched in horror and I stand in solidarity with the Back Lives Matter campaign," she said.
"But I would ask people to please act responsibly. Gathering in such big crowds, we're spreading the virus. Ultimately, that's killing people."
Health Minister Robin Swann said the time is not right for mass protests.
"No matter how just your cause is, at this minute in time it should not cost or threaten someone else's life," he said.
"There will be a time in Northern Ireland where protests will go back to being just and allowed. Now is not that time."
Chief Constable Simon Byrne said he was "appalled at actions of the former officers from Minneapolis PD, but public protests at this time will endanger lives".
Appearing before the Policing Board, he defended the PSNI response. "Sometimes it's getting that fine line right because what to one person is strong enforcement and being robust, to other people is aggressive and oppressive, and it's difficult to make these decisions in real time," he said.
Assistant Chief Constable Alan Todd, who has responsibility for the enforcement of the Covid-19 regulations, said the approach to policing the next planned protest on Saturday is being developed.
He said no action was being taken against organisers of the last rally as "the expenditure of thousands of hours of police time in seeking to put these matters before the PPS is unlikely to be proportionate in all the circumstances".
Protest organiser Jolene Francis said: "I agree that [at] the epicentre of the protest that there were people gathered together. They were incredibly emotionally charged. We didn't realise how big the turnout would be.
"I do regret not being able to enforce social distancing as heavily as it should have been, but I'm still very proud of the people who were there."