The body representing prison officers in Northern Ireland have called for three senior managers to resign.
The Prison Officers' Association said they had no confidence in Robin Masefield, Mark McGuckin and Max Murray.
It follows concerns over the handling of staff disciplinary action following the suicide of inmate Colin Bell.
In a statement Mr Masefield, who is the head of the service, said he regretted the approach being taken by the POA.
The POA has claimed those disciplined were denied "natural justice" during the investigation.
Mr Masefield said that the POA was operating a withdrawal of goodwill across the prison estate over the dispute and that this was "having an adverse impact on prisoners and on their families".
He said that "every individual has a right to an appeal in line with the procedures" and that the POA wanted "a pre-determined outcome to the appeal process and management has made clear that it will not interfere in that process".
The head of the Prison Officers' Association Finlay Spratt said that he was not opposed to his members being disciplined if a breach in their code of conduct had occurred but that "agreed procedures" had to be followed.
He said that members had been working to their "terms and conditions" since Monday.
"When a new justice minister is appointed we will be advising him that change is needed at the very top of the prison service," he said.
The governor and deputy governor at Maghaberry were replaced after a review into the death of Bell, but did not face disciplinary action.
Bell who was serving a life sentence for murder, hanged himself in 2008.
An earlier report found some staff who were supposed to be monitoring him were lying in bed watching television while they were supposed to be on duty.
Bell, who had a history of self-harm, was on suicide watch and was meant to be monitored every 15 minutes.
The Prisoner Ombudsman Pauline McCabe published a damning report on the regime in the wake of the death.