The Mater Hospital in Dublin is at the centre of an investigation into why more than 200 cases of Covid-19 were notified to the Department of Health for the first time yesterday.
He said they dated back to mid-March.
It has now been confirmed that the hospital in question is the Mater Hospital and the number of cases is 244.
However, the hospital said it had reported all cases of positive results to the relevant authorities on a daily basis.
It said it was working with the Health Service Executive to understand why the provided data may not have been accurately captured.
The HSE said it was not yet in a position to confirm whether the hospital did or did not report the cases.
It said the issue was currently under review with the Ireland East Hospital Group and the Mater Hospital.
Covid-19 has been a notifiable disease under infectious diseases legislation since February.
A medical practitioner or medical officer in a hospital must notify the authorities of a case of infectious disease "forthwith".
It is understood the cases in question relate to healthcare workers at the hospital who would be assessed by the hospital's occupational health department.
It is understood positive cases in healthcare workers in the hospital are notified to the HSE separately to cases involving patients.
In a statement, the hospital said it had reported all cases of Covid-19 positive results to the relevant authorities on a daily basis.
It said at all times the hospital provided the information the HSE required and met all legal requirements to report infectious diseases. It said all of this information is correct and up to date.
It added that it was working with the HSE to understand why the provided data may not have been accurately captured.
The hospital went on to say that it had carried out comprehensive contact tracing on every member of staff who tested positive for Covid-19 through its occupational health department.
It said more than 300 staff at the hospital had tested positive and a further 1,500 had self-isolated following contact tracing.
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Minister for Health Simon Harris, speaking at the press briefing on the next phase of the road map to easing of Covid-19 restrictions, said was "noting" the statement provided by the Mater.
But he has not received assurances about the level of contact tracing that has been carried out.
Mr Harris said: "It is a matter for Paul Reid and the HSE to provide assurances to me and the department and that work is underway now."
Speaking earlier today before the morning's Cabinet meeting, the Minister said he was waiting for a full report from the HSE into the matter.
He said the rules around the reporting of infectious diseases were very clear and he said the reporting of cases as far back as the middle of March was "extremely disappointing".
Mr Harris said whether or not it was a criminal matter, needed to be checked.
He said there was a legal requirement to disclose and the legislation was very clear on who the burden of reporting tests rested with.
He acknowledged that people were working very hard in hospitals and laboratories, but there was a reason why the requirement was there.
