Minister for Health Leo Varadkar has met with families affected by adverse incidents in the maternity unit at the Midland Regional Hospital in Portlaoise.
It is understood Mr Varadkar reiterated an apology to the families for the loss and experiences they have suffered.
Up to 100 people attended the meeting with Mr Varadkar, who was accompanied by Chief Medical Officer Dr Tony Holohan and Dr Susan O'Reilly, CEO of the Dublin Midland Hospital Group.
The families were briefed on the changes implemented at the hospital.
Mr Varadkar said the hospital is now much safer but a lot of work remains to be done.
He also told the meeting that he will discuss with Minister for Justice Frances Fitzgerald whether the law of criminal negligence can be strengthened in cases of medical negligence.
During the meeting families spoke openly and at times angrily about their dissatisfaction with progress to date investigating their cases.
The meeting follows a similar one with families last May.
Róisín Molloy, whose son Mark died died shortly after he was born at the hospital, said it was a very positive meeting.
She said, however, that there are still issues which are ongoing for a number of families, adding "we have HSE investigations, we have external investigations that are ongoing but accountability seems to still be an issue for many of us that have lost children in Portlaoise hospital".
A number of families whose cases have been investigated in the wake of an RTÉ Investigations Unit report into baby deaths at the hospital expressed their anger that many of their questions remain unanswered.
Mr Varadkar said the number of midwives at the hospital has increased from 39 to 70 and it is probably now one of the best staffed hospitals in the country.
He said management are currently looking to recruit two more obstetrician gynaecologists and two neonatologists to work between the Coombe and Portlaoise hospitals.
All staff have now been trained fully in the use of equipment used to monitor the foetal heartbeat.
A full quality and patient safety team is now also in place at the hospital and patient safety surveys are being conducted to judge user satisfaction.
No serious reportable or preventable deaths were reported at the hospital last year.
The meeting between Mr Varadkar and the families lasted more than three hours.