Taoiseach said today that this is a "harrowing time" for the families of four babies who died at the Midland Regional Hospital in Portlaoise.
There have been demands for an independent inquiry after a TV documentary highlighting the deaths over a six-year period at the facility.
The infants died shortly after they were born, even though they didn't have any abnormalities when their mothers went into labour. The HSE has apologised for shortcomings in their cases.
The Health Minister has requested a full report on the facility.
Speaking in Cork this morning, Taoiseach Enda Kenny said he would wait to see the details of that before deciding on a public inquiry.
"Clearly, the inefficiencies that were here and that resulted in the death of a number of babies is very sensitive for those families," he said.
"But I hope that the changes that have already been introduced - and will be further followed through now with a report from the Minister will bring about that situation".
James Reilly said he found the revelations in the television documentary on the cases upsetting, disturbing and shocking.
"What's happened … you can't say inexplicable because there will be an explanation – but it won't be an explanation that I will find acceptable … from what I've seen."
"Maybe in saying that I'm displaying, perhaps, more pre-judgement than I should, but I find it shocking."