Officials have asked people to be patient as they work through the backlog and roll out additional resources.
So far, 90 suspected cases have been tested in Ireland but all have come back negative.
Eight hundred women were affected by the glitch at a US lab.
The HSE has been aware of this error since November but it was only made public two weeks ago.
The HSE is encouraging people to go to their GP where possible, instead of attending hospitals.
Fianna Fáil has said that the delays are leading to overcrowding in emergency departments.