Black community leaders have vowed to keep pushing for an apology despite reaching a "stalemate" with police over how they handled last month's Black Lives Matter rallies.
Dr Livingstone Thompson, of the African and Caribbean Support Organisation NI (ACSONI), said the PSNI had shown "poor judgment in their application of the law" by fining protesters in Londonderry and Belfast.
Meanwhile, North West Migrants Forum said police had caused "deep offence" by "selectively" issuing penalties.
A PSNI spokesman said they were aware of "anticipated legal proceedings" as well as a judicial review, and it would be "inappropriate to comment further".
Policing of Covid-19 regulations is also being investigated by the Ombudsman. But in a previous letter to the group, which includes ACSONI, Chief Constable Simon Byrne said penalties would not be dropped.
Dr Thompson said such a move would be "symbolic" to the community, who felt they had been treated unjustly.
He added: "The optics of it is important because it would indicate that the community is not blind in its perception of unfair application. It is a recognition of not only the right they have to assert the issues, but it would mean the individuals involved in any case would not have to worry about the process."
The PSNI said: "The Police Ombudsman's Office is carrying out an investigation into how the police have enforced the Coronavirus Public Health Regulations at large public gatherings and the Northern Ireland Policing Board have also commenced a review of the police response to Covid-19.
"We are also aware of anticipated legal proceedings in relation to protests on June 6, as well as a forthcoming judicial review.
"We welcome the independent oversight of police actions and as these matters are ongoing, it would be inappropriate for the Police Service of Northern Ireland to comment further at this time."
Black community organisations have twice met with the PSNI since the June 6 rallies.
Dr Thompson said: "The PSNI, and organs of the state, must work hard to achieve diversity in its decision-making, for that is a place to start to mitigate the impact of unconscious bias, not least in the application of the law."
He said the new generation of activists were prepared to push for real change - and "not to put up with expressions of hurt".
Last week Derry and Strabane District councillors voted to condemn the PSNI's enforcement action and for all fines and threats of legal action to be dropped.