HSE Director General Tony O'Brien told HIQA that its findings in relation to Portlaoise Hospital implied a reckless endangerment of patients.
After receipt of a draft report, in a reply on 13 February to HIQA, Mr O'Brien said the draft findings would shatter confidence in the HSE to deliver services.
He said that HIQA had to afford affected parties fair procedures to deal with the findings in the draft report.
The HSE published its correspondence with HIQA this evening.
It published five letters on its website that it sent the agency seeking further information and supporting documentation to allow its staff respond to issues raised about deaths of babies at the Midland Regional Hospital.
The HSE told HIQA its draft report has over 250 adverse findings or inferences.
The executive said HIQA has no power to make findings which attribute or infer blame, guilt or liability to anyone in the HSE.
The publication of the report by the Health Information and Quality Authority into baby deaths at the hospital has been delayed due to legal issues with the HSE.
The HSE has rejected any characterisation of its engagement with HIQA as menacing.
Minister for Health Leo Varadkar earlier said he does not want to see HIQA and the HSE suing each other over the Midland Regional Hospital Portlaoise report.
He said this would be a waste of time and taxpayers' money and he said it was important to allow due process.
Minister Varadkar said that both parties had agreed a bilateral process to allow the report be published sooner rather than later.
A draft of the report was recently circulated by HIQA to various affected parties for their observations.
The HSE has raised the possibility of legal action if the report is published in its current form.
It has sought further information and documentation from HIQA on the draft report.
The report has to go to the HIQA Board for approval and then to the Minister for Health before publication.
An investigation into the Midland Regional Hospital in Portlaoise was set up over a year ago by former health minister James Reilly after five baby deaths in the maternity unit between 2006 and 2012.
It followed a report by RTÉ's Investigation Unit which raised questions about the unit.
HIQA appointed a six member team to examine the matter and its draft report was finished recently.
During the course of its investigation, HIQA was contacted by, or was supplied with information from 83 families, regarding their concerns about issues at the Midland Regional Hospital Portlaoise.
HIQA is to give more information to those named in its report with regard to its findings.
The draft report suggests some of the blame for what occurred was due to shortcomings in senior HSE corporate management.
It highlights constant changes in corporate structures in the service, as well as a lack of clear reporting relationships, as contributory factors.
The draft report says that while Portlaoise is listed as a regional hospital, it was funded at a lower level as a local hospital.
In a statement the HSE said many members of staff had participated in the investigation.
It said a full draft report was presented to the director-general of the HSE on 2 February.
"The Draft Report contained some factual inaccuracies, lacked context and balance and failed to give reasons for or to substantiate certain findings relating to parts of the HSE and/or certain individuals.
"On further examination the DG noted that these individuals had not been furnished with the relevant information or documentation in order to allow them to appropriately respond to these findings.
"Consequently, on February 13th, the DG wrote to HIQA assuring it of the HSE's desire to assist and co-operate in completing a more contextual and procedurally fair report and seeking a meeting to address shortcomings in the process."
The HSE said that HIQA declined its offer to meet or to provide further information and supporting documentation to help to respond to the findings.
It said the HSE wrote three more letters seeking a meeting and further information from HIQA, but said the authority did not take up these requests.
"At that juncture the HSE gave consideration to seeking court intervention in order to ensure that a more balanced and fair final report would ensue with appropriate input from HSE staff members who have had access to all of the relevant documentation from HIQA."