Sinn Féin leader Mary Lou McDonald has refused to apologise for voicing opposition to any current police commander in Northern Ireland succeeding the retiring chief constable.
She said she would not be retracting her controversial comments about who should replace George Hamilton when he steps down in June.
Ms McDonald has faced calls to apologise from a policing representative body while her comments have also sparked a wave of condemnation from political rivals.
Addressing the media in Dublin today, she said: "There's nothing to apologise for, there's no retraction to be made."
Ms McDonald said she would have no role in appointing the new chief constable.
The PSNI's oversight body - the Policing Board - makes the appointment. A Sinn Féin member 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," she said.
"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 Féin appointee behaves in that manner."
Ms McDonald characterised the controversy as "political huffing and puffing".
Meanwhile, Fianna Fáíl has described Ms McDonald's comments as "wholly irresponsible" and "very, very dangerous."
It said the comments call into question whether or not the party supports Garda Commissioner Drew Harris.
The party's spokesperson on housing, Darragh O'Brien said Sinn Féin is "trying to undermine a police service and it does have a real chilling effect across both communities but in particular, the nationalist community that has worked very hard over the last 20 years to work with the PSNI to change the structures of the PSNI".
He said: "That hasn't been easily won, a remark like that is a very dangerous one.
"It is a wholly irresponsible one and it is an immature one as well. I think it should be retracted."