Patient Focus is calling for an independent inquiry into the deaths of four newborn babies at the Midland Regional Hospital in Portlaoise.
An RTE Prime Time documentary looked at the deaths which occurred over a six year period - it revealed the infants died shortly after birth, although they were not suffering from any abnormalities at the onset of labour.
The HSE has apologised for shortcomings in the cases and the National Director of Acute Hospitals, Ian Carter, will arrange to meet the families.
Whilst the Minister for Health James Reilly has requested a full report.
Patient Focus says an independent investigation is needed - one that goes back as far as 10 years and examines care in all maternity units.
Spokesperson Bridget Doherty says an apology from the HSE isn't enough: