The HSE says it, and the Midland Regional Hospital in Portlaoise, accept that there were shortcomings in cases involving the deaths of a number of new babies.
RTE's Prime Time programme investigated deaths at the maternity unit in the hospital, over a six-year period.
The babies were alive during the onset of labour, but died during birth or a few days later.
A report into the death of one baby in 2008 found a number of failings in care provided by the hospital to both the mother and baby, including a failure to recognise when a baby was in distress during labour and the imappropriate use of a drug used to increase the rate of contractions.
In a statement, the HSE said there were unacceptable delays in completing reports, communicating with families and acting on recommendations.
The HSE and the hospital apologised unequivocally to the families for those failings, and the National Director of Acute Hospitals will arrange to meet the families to discuss their cases.