Sinn Fein president Mary Lou McDonald has been accused of making a "grave miscalculation" after she said she has no confidence in any senior PSNI officer being able to take over the role of Chief Constable.
The chair of the Police Federation for Northern Ireland, Mark Lindsay, also called on Ms McDonald to apologise for her comments in Belfast yesterday after meetings with top officers and the Police Ombudsman.
Mr Lindsay described her statements as "wholly inappropriate and offensive".
The PSNI has faced heavy criticism in recent days after it emerged it had failed to disclose a number of documents to the Ombudsman in relation to the 1992 Sean Graham bookmakers massacre.
Five people were killed when UFF gunmen opened fire inside the Ormeau Road premises.
The PSNI has apologised and blamed the omission on human error.
Appearing alongside several people who had family members killed by loyalist terrorists, Ms McDonald said the police now had "zero credibility" when it came to dealing with legacy cases.
She said the "very cynical strategy and policy of withholding information" had dealt another blow to nationalist confidence in the force.
She added: "We've asked the PSNI to tell us what else they're hiding, what else they're failing to disclose."
With Chief Constable George Hamilton due to retire this summer, Ms McDonald said there was no credible internal candidate to take over.
"Is there somebody specific inside the PSNI, is there somebody inside who should be the Chief Constable?" she asked.
"I have to answer honestly that no, I can't identify such a person.
"Lots of this is about who leads, who is in the top job within the policing, but it goes much broader than that.
"This is an issue about the culture of policing, it's about their systems and it's about their capacity to be held fully accountable."
Ms McDonald also made a direct appeal for Taoiseach Leo Varadkar to intervene in the scandal, and added that the British Government was "bang in the centre of this whole sorry, sordid escapade".
PFNI chairman Mr Lindsay accused Ms McDonald of "extraordinary interference in an open and transparent selection process".
"Sinn Fein's representatives on the Northern Ireland Policing Board will have a role to play in deciding on Mr Hamilton's successor, and to adopt this public position now is wholly inappropriate, offensive and ill-judged," he stated.
"Her comments will call into question the objectivity and credibility of Sinn Fein representatives who will be involved in that selection process.
"Her comments have placed her party's representatives on the Policing Board in a difficult position and in the interests of fairness to senior PSNI officers who might put their names forward for the post, I call on the Sinn Fein President to reflect on her grave miscalculation and apologise.
"Senior officers in the PSNI do not deserve to be treated as some second-class candidates in this competition.
"They are people of integrity who work for the entire community and should not be disadvantaged in this manner.
"For Sinn Fein to attempt to interfere in a properly run selection process does nothing to enhance the party's stated position on fairness and equality."
DUP Policing Board member Mervyn Storey MLA said he had written to the chief executive of the Policing Board to seek legal advice about Ms McDonald's statement.
"This is a very foolish comment," he said.
"There are many capable officers in the PSNI and to make such a blanket statement is an outrageous generalisation.
"Policing Board members will be responsible for interviewing and assessing any future Chief Constable.
"How can any Sinn Fein member sit on that panel and candidates from the PSNI expect to get a fair hearing?
"Anyone sitting on that panel must be fair and open-minded rather than having a pre-determined outcome."
Ulster Unionist Policing Board representative Alan Chambers raised questions over whether Sinn Fein is preparing to withdraw support for policing.
"Mary Lou McDonald needs to be very careful in what she says," he stated.
"The selection of a new Chief Constable is a matter for the Policing Board.
"In saying that the new Chief Constable of the PSNI should come from outside the force, she is not only displaying a lack of faith in the officers there already, she is opening up the possibility of legal action and employment tribunals from unsuccessful candidates, who could point to bias on the part of Sinn Fein members of the Policing Board.
"There will be genuine concerns that this is Sinn Fein's way of signalling that it is preparing to withdraw support for policing in Northern Ireland.
"You have to wonder just who Sinn Fein would find acceptable to fill the role of Chief Constable, especially when you recall their opposition to the Appointment of Drew Harris as Garda Commissioner.
"You would almost think they don't want to be policed by anyone."
Meanwhile, Alliance Policing Board member John Blair questioned whether Sinn Fein can remain on the interview panel to select a new Chief Constable.
"This was a careless and irresponsible thing to say," he said.
"It would be the ideal scenario to have as broad a representation as possible on the selection panel which interviews candidates and decides upon George Hamilton's replacement.
"However, this intervention from Mary Lou McDonald now begs the question as to whether any Sinn Fein representative can sit on that panel."
A Department of Justice spokesperson said: "The Northern Ireland Policing Board is putting in place a process for the appointment of a Chief Constable. It is important to attract the best candidates from all quarters for this important and challenging role."
Policing Board chair Anne Connolly said that the selection of a new Chief Constable would be based on "merit, fairness and openness".
"The appointment of a new Chief Constable is a priority for the Northern Ireland Policing Board," she stated.
"The selection and assessment processes will be based on the key principles of merit, fairness and openness.
"This is a significant leadership position and the board will want to attract a wide range of candidates."
Mrs McDonald's comments came after she met bereaved families caught up in a controversy involving the PSNI's failure to disclosure documents about historic killings.
Marian Walsh's son Damien was 17 when he was murdered by UFF terrorists in Twinbrook in 1993.
"It's 26 years now since we lost him, it's been a very difficult time," she said.
"Fifteen years ago I went to the Police Ombudsman's Office and I'm still waiting for his report. Apparently it's now with the PSNI so they can check the facts in it. It looks like it's going to be put back again."
Thomas Duffin's father Jack was one of the five victims of the Sean Graham's bookies atrocity.
Speaking after meeting with the PSNI, he said: "They didn't come back with anything we didn't already know.
"The family has just been thoroughly demoralised.
"We thought we were on the verge of getting a report out from the Ombudsman.
"Now we don't think it's going to happen.
"We think it's a total disgrace what they've done."