The HSE has published its correspondence with the health watchdog on a draft report into the deaths of a number of babies at Portlaoise hospital.
In one letter, the Director General of the HSE Tony O'Brien said he does not agree with a number of the findings and the process used in the investigation.
He said it is vital people have confidence in the HSE to deliver vital services in a timely and appropriate manner, and the draft findings would "shatter" that confidence.
In another, Mr O'Brien said it appears that there are more than 250 adverse findings or inferences in the draft report.
However, he claimed that the HIQA had no statutory authority to "attribute or infer blame, guilt or liability to any individual or set of individuals employed by … the Executive".
He also said HIQA had not allowed the staff members - who he said could be easily identified from the report - the opportunity to respond to the allegations, therefore denying them fair process.
He also claimed the report had a "lack of accuracy, context, specificity, and balance" with comments that serve no purpose other than "to cause needless distress and damage."
Yesterday, it emerged that the HSE had considered seeking a court order delaying publication of the report, a fact detailed in the most recent of the letters.
The letters were released on the HSE's website last night.
Both parties are now attending meetings in an effort to resolve the issue, rather than head to the courts.
Fianna Fáil said the row is an insult to those involved in and depending on maternity services.
"We've had Mr O'Brien … publishing letters on the HSE website," said party health spokesman Billy Kelleher, demanding Minister Leo Varadkar direct the HSE to allow HIQA to do its job.
"I'm beginning to think: is this now a PR battle? That's very distasteful, it's very destructive, and more importantly they seem to forget that five babies died tragically in Portaloise hospital."
Commenting on the furore, Enda Kenny said the Minister was right to intervene, rather than allow the two bodies to use public money in court proceedings.