A phone line has been set up at the Midland Regional Hospital Portlaoise to deal with concerns arising from last night's 'Fatal Failures' programme by RTÉ's Investigation Unit.
The documentary looked at the deaths of four babies over a six-year period at the hospital.
The helpline (057-8696076) was open from 9am to 5pm today and will also operate at the same times on Saturday and Sunday.
Callers are being asked to leave their name and number on voicemails.
The HSE said details from each call will be documented and, if requested, a clinician will review the medical notes and a return call will be made "at the earliest opportunity".
Minister for Health James Reilly has apologised to the families affected by the failures at the hospital.
Mr Reilly said he found last night's report upsetting and disturbing.
Speaking to reporters while on a visit to Naas General Hospital, he said it was unacceptable that patients had not been told their cases were being investigated.
He said he is appalled that two patients are still not aware of investigations and he has asked that they be contacted today as is their due right.
Elsewhere, Taoiseach Enda Kenny said although he had not seen the programme, it was a harrowing time for all the families involved.
At an event in Co Cork, Mr Kenny said the report has been referred to Mr Reilly for a full analysis about what happened and it would not be appropriate to comment on calls for a public inquiry until such a process is complete.
It emerged earlier that the midwifery staff at Portlaoise wrote to two ministers in 2006 expressing concern over staffing levels at the hospital.
In the 2006 letter to then minister for finance Brian Cowen and then minister for health Mary Harney, the hospital's midwifery staff said they had "a real fear" that a mother or baby will die in their care before these issues are addressed.
In the letter, seen by RTÉ's Investigation Unit, they also said they had made their concerns known to management on a number of occasions but that nothing had happened.
The letter was written prior to all of the deaths of babies examined in last night's documentary.
The babies died in similar circumstances over a six-year period at the hospital.
They were all alive at the onset of labour, but died either during labour or within seven days of birth.
Last night, the Health Service Executive apologised unequivocally to the families.
It also accepted that there were serious shortcomings, including unacceptable delays in communicating with families, and acting on recommendations.
Laois Fine Gael TD Charlie Flanagan has called on the HSE to make full disclosure on the circumstances surrounding the deaths of all babies at the hospital's maternity unit.
Women reassured about maternity services
Obstetricians have moved to reassure women about maternity services in Ireland.
Consultant obstetrician and gynaecologist Professor Fionnuala McAuliffe, who is also a spokesperson for the Institute of Obstetricians and Gynaecologists, has expressed her sympathies to the families.
In a statement this afternoon, she said the families have suffered greatly and added that "the death of every baby is an absolute tragedy and very traumatic for families".
Professor McAuliffe said pregnant women who may be worried today should have confidence in the maternity services.
She said: "Ireland is a very safe country in which to have a baby. We have low rates of perinatal deaths when compared to neighbouring counties, such as the UK or France."
However, she said that while "we have good outcomes in our maternity services, when things go wrong, we must learn from our mistakes".
Professor McAuliffe said last night's programme highlighted a lack of open communication.
Maternity services are understaffed and under-resourced, she said, and there is a need for more resources to maintain and improve standards of care.
She said existing resources must also be maximised.
Professor McAuliffe said they would continue to improve maternity services and to maintain the low rates of maternal and perinatal mortality.
Earlier, Patient Focus called on senior management at the hospital to come out and allay the fears of women due to give birth there.
Sheila O'Connor said management needs to outline what has been done in the hospital since the death of these babies.
Speaking on RTÉ's Morning Ireland, Ms O'Connor said it is important that the people on the ground at the hospital comment.
She said: "I think the only way to allay this, and I have no doubt whatsoever about the sincerity of Dr Philip Crowley when he apologises for the HSE, but unfortunately he is not the person on the ground in Portlaoise.
"I think what really needs to happen is that management, clinical director people, directors of nursing and midwifery need to come out and reassure people in the area who are going to be using this hospital in the near future."