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Published 13:51 29 Mar 2019 GMT
Updated 15:13 29 Mar 2019 GMT
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The hospital has described the deaths as a "tragic occurrence" and announced that it would be carrying out its own investigation into what happen.
Announcing the review, Minister Simon Harris said that such an investigation is now standard in cases like this.
He also offered his condolences to the family of Ms Downey.
"This is an extraordinary tragedy," he said.
“It is just so upsetting and devastating to have a mother and her newborn son pass away in one of our hospitals."
The funeral of Ms Downey and baby Darragh in Ballyagran, Co Limerick on Saturday.Explore more on these topics: