Mary Lou McDonald has declined to apologise for voicing opposition to any current police commander in the north succeeding the retiring chief constable.
The Sinn Féin president said she would not be retracting her controversial comments about who should replace George Hamilton when he steps down in June.
"There's nothing to apologise for, there's no retraction to be made," said Mrs McDonald, dismissing criticism of her remarks as "political huffing and puffing".
The republican leader said she would have "no role" in appointing the north's next police chief and said the Sinn Féin representative on the recruitment panel would act in accordance with the rules and regulations.
The Police Federation representative body has demanded an apology from Mrs McDonald, while her comments have also sparked a wave of condemnation from political rivals, who claim she has compromised the recruitment process.
The body that oversees equality laws in Northern Ireland - the Equality Commission - has also voiced concern about her remarks.
Sinn Fein leader Mary Lou McDonald says Irish government needs to intervene to reassure families let down by PSNI failures over Sean Graham bookies massacre: pic.twitter.com/X58ygucayC
— Q Radio News (@qnewsdesk) February 18, 2019
On Monday in Belfast, Mrs McDonald said she would not have confidence in any current member of the PSNI's senior leadership team taking the helm of the organisation.
Her comments came after she met bereaved families caught up in a controversy involving the PSNI's failure to disclose documents about historic killings to the Police Ombudsman.
The PSNI's oversight body - the Policing Board - is responsible for appointing the chief constable. A Sinn Féin appointee will be on the board panel that makes the decision.
"On the issue of the chief constable, I have no role in the appointment of a chief constable," the Sinn Féin president said this afternoon.
"I was asked could I identify someone from the senior team who I thought ought to be chief (constable) and the truth is I can't.
"Be clear on this, I am not going to decide who the chief constable is. Yes, we make appointments to the Policing Board and when people are appointed to the Policing Board they act in accordance with the statutory scheme, the rules and regulations - the letter of them.
"And I would expect and insist that any Sinn Fein appointee behaves in that manner."
The original comments came during a press conference in south Belfast during which she claimed the PSNI had "zero credibility" in its handling of cases linked to the legacy of the Troubles.
Mrs McDonald was asked if she had confidence in any of the current leadership team to replace Mr Hamilton.
"No I don't," she replied.
"The PSNI's credibility on matters pertaining to legacy is zero, I don't think that happened today or yesterday but I think certainly this turn of events has confirmed that."
In response to a follow-up question on the same issue, the Sinn Fein leader added: "Is there somebody inside who I think should be the chief constable, and 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 in policing, but it goes much more broad than that. This is an issue of the culture of policing, it's about the systems and it's about their capacity to be and to be held fully accountable."
Last week, it emerged that the PSNI failed to disclose "significant information" relating to a notorious loyalist mass shooting.
Police Ombudsman Michael Maguire said "significant, sensitive information" around the incident at a bookmakers in south Belfast was not made available to his investigators.
Five people were killed on February 5 1992, when members of the UFF opened fire on the Sean Graham bookmakers shop on the lower Ormeau Road.
Dr Maguire's office said the non-disclosed material, which it has now obtained, has opened new lines of inquiry in its investigation into the Ormeau Road shootings, as well as activities of loyalist paramilitaries in the north west between 1988 and 1994, and its probe into the murder of teenager Damien Walsh at a coal depot in west Belfast in 1993.
Last week, PSNI Deputy Chief Constable Stephen Martin apologised on behalf of the police and said they never sought to withhold the information from the ombudsman investigators, putting the incident down to human error.
During the press conference in Dublin today, Mrs McDonald was pressed on whether she had confidence in current Garda Commissioner Drew Harris, a former high-ranking PSNI and RUC officer.
"I do, yes," she said.
"He has a job to do and I want him to succeed."
