HSE chief Tony O'Brien was under pressure to step down last night in the wake of a damning report into patient care at Portlaoise Hospital.
Róisín Molloy, whose son Mark died shortly after his birth at the hospital in 2012, said: "I think he should be one of many to resign. We need a complete clear-out and a proper running, functioning HSE."
Mrs Molloy said the report from health watchdog Hiqa demonstrated that senior HSE officials were warned the maternity services at Portlaoise were unsafe but recklessly allowed the situation to continue.
However, Mr O'Brien insisted he would not be resigning. "The bulk of the events, not all of them, happened before I was in my present role. I came into this role at the request of the then Minister for Health to make a range of changes to the HSE," he said.
"That has included making quite difficult choices to divert resources from some areas into acute hospitals to address some of the issues identified in the report. My view is that the actions I took are the right actions."
Responding to calls for accountability by senior HSE staff, Health Minister Leo Varadkar said Hiqa spent a year completing the report and did not make findings against any individual.
"I only received the report on Wednesday and I am not going to make myself judge, jury and executioner. But I do expect the HSE to take corporate responsibility for implementing the report's recommendations and also learning from it," he said.
But launching the report yesterday, Hiqa chief executive Phelim Quinn said it was now a matter for the Government to seek accountability.
The investigation team, which examined safety standards after it emerged that five babies had died of lack of oxygen after signs of foetal distress were not recognised or acted on, said three more baby deaths are also to be examined.
The cases have been referred to a review which is being carried out by Holles Street obstetrician Peter Boylan, who has examined the first 28 medical charts of babies whose parents raised concern in the wake of the Portlaoise revelations.
Dr Susan Reilly, head of the Dublin Midlands Hospital Group, which includes Portlaoise, said the first set of parents whose reviews are completed will receive correspondence in the coming weeks.
She said several actions have been taken to make Portlaoise Hospital safe, including the appointment of a new manager and a director of midwifery.
More doctors and nurses have been hired and complex cases in the maternity unit, which is being linked to the Coombe Hospital in Dublin, are now transferred.
Portlaoise patients interviewed by the Hiqa team spoke of traumatic experiences, including being told in a hospital corridor that their baby had died. One woman said she was reprimanded for crying after her baby's death.
Others were told their baby was stillborn, only to discover in documentation or reports that this was not the case.
Parents in some instances had their baby brought to them in a metal box on a wheelchair covered with a sheet and pushed by mortuary staff.
They described a lack of compassion, empathy, dignity and respect.
A key recommendation of the Hiqa report is the setting-up of a patient advocacy service to work on behalf of patients and families seeking answers about death and injury.
The investigation team said it could not give guarantees that other similar hospitals were not failing in patient safety care.
It was essential that the Department of Health develop a national maternity services strategy for Ireland, originally called for in another Hiqa report in 2013.
Patient safety advocate Margaret Murphy, who was on the investigation team, said: "To err is human, to cover up is unforgivable but to refuse to learn is inexcusable."
Mr Varadkar is expected to visit Portlaoise Hospital next Wednesday and meet some of the families involved.
Krysia Lynch, of the Association for Improvements in Maternity Services, said there was gross under-staffing and under-funding of maternity services across the country, as well as a lack of accountability and oversight.
The Hiqa investigation team has clearly carried out a thorough and devastating review of the performance of the HSE and local management of the Midland Regional Hospital, Portlaoise over the last number of years and the findings cannot make easy reading for those who are responsible for the management of the hospital.