Fianna Fáil has said that it is disappointed that an insider has been given the top job in the HSE.
The Health Minister has appointed Tony O'Brien the new Director General of the Health Service Executive.
It comes after the man who formerly held that role - Cathal Magee - offered his resignation last week.
Fianna Fáil's spokesperson on Health, Billy Kelleher, said that the role should have been open to competition.
There has been criticism too from The Pro Life Campaign Group, who said that Mr O'Brien has a history as a leading campaigner for abortion in Ireland.
However Minister Reilly said that he has full faith in Mr O'Brien.