Sinn Fein has said that a "continuous pattern of bad policing" raises fundamental questions for the entire PSNI senior leadership team, and not just the Chief Constable.
But the DUP said that criticism of police from Michelle O'Neill's party "rings utterly hollow" given its "antics at the Storey funeral and disregard for Covid-19 rules".
The Chief Constable met Sinn Fein, the DUP and SDLP yesterday in an attempt to defuse tensions following the arrest of a victim at the commemoration for the Sean Graham bookies massacre in south Belfast.
The PSNI was captured on camera on Friday handcuffing Mark Sykes who was injured in the 1992 UDA attack. The Police Ombudsman is investigating the incident.
Simon Byrne has insisted he won't be resigning over the matter for which he has apologised. He has suspended one officer and repositioned another.
Justice Minister Naomi Long said that the Chief Constable retains her confidence. Writing in An Phoblacht, Sinn Fein junior minister Declan Kearney said the question of Mr Byrne's resignation was a diversion from the real issue.
"The deepening crisis of confidence in the PSNI and widespread anger about the continuous pattern of bad and differential policing now raise fundamental questions for the entire senior leadership team of the PSNI, not just its Chief Constable," he wrote.
"This extends to the PSNI institutional culture, human rights' ethos, organisational training, adherence to the principles of the Good Friday Agreement, and commitment to the vision of our peace process."
Mr Kearney said that successive chief constables, and their leadership teams, had "failed to internalise the priorities and requirements of policing in our society as it continues to emerge from conflict".
"For 80 years the RUC was a pillar of the exclusionary, apartheid system, which was the northern state.
"The formation of the PSNI was meant to be a break with that past. The PSNI leadership has a lot of convincing to do within this community, that it is serious about transformative policing, and is indeed up to the task," he added.
Ms O'Neill said there were "frank exchanges" during her party's meeting with Mr Byrne.
"I made it clear that the arrest of a victim laying flowers on the anniversary of the Ormeau Road massacre, and the PSNI's failure to intervene as dozens of masked UVF members roamed the streets, have created a crisis in public confidence in policing.
"I left the Chief Constable in no doubt that the events of recent days are a watershed moment for policing and public confidence in policing."
But speaking after her meeting with Mr Byrne, the DUP leader said PSNI decision-making must be "based on the law and not politics".
Criticising his handling of the controversy, Mrs Foster said: "The swift response by the Chief Constable has all the hallmarks of trial by social media, and of two young officers being scapegoated.
"This will inevitably cause alarm among those starting their career in the police.
"The matter has been referred to the Police Ombudsman. Decisions about the matter should have been made at the completion of that investigation."
Police have said that up to 40 people were present at the Lower Ormeau commemoration on Friday when only six are permitted to gather outside under Covid regulations.
But Relatives for Justice said that no more than 15 people were on the street, socially distanced and in household bubbles.
Mrs Foster said: "The anniversaries of atrocities at Kingsmills and Teebane were marked respectfully and lawfully.
"There is a duty on all organisers to act in compliance with the law.
"While we understand the need for a proportionate and sensitive policing response, operational decisions must be fair and balanced. There should be no apology for enforcing the rule of law."
Ulster Unionist Policing Board member Mike Nesbitt asked if the officers at the bookies commemoration followed the policy of "engage, explain, encourage, enforce".
He said: "The second set of questions is directed to the Chief Constable and his leadership team. Did he act precipitously in suspending one of the officers, given the Ombudsman is on the case?
"Thirdly, while I respect dignified commemorations, there is a question over whether the event organisers fully complied with the Covid regulations and guidance.
"Recently, my party marked the 40th anniversary of the murders of former Stormont Speaker and Somme veteran, Sir Norman Stronge and his son James by the Provisional IRA. We did so with only two people representing the party at the memorial engraving in Parliament Buildings."
Criticising Sinn Fein's response to the controversy, Mr Nesbitt added: "Politicians must avoid the urge to use Friday's events to be divisive and drag us backwards. Instead, we must learn lessons and move forward together."
SDLP leader Colum Eastwood said: "It is difficult to watch the footage of the last week and not be angry. But that frustration with how the PSNI has managed events should be channelled through the police accountability structures. We cannot allow the actions of a few to destabilise the progress we've made. The SDLP will be pursuing these issues through the Policing Board as a matter of urgency."