Testing centres across Ireland fully reopened after some were closed or scaled back over the Christmas period.
The HSE has also fully reopened vaccination centres.
A further 6,735 cases of Covid-19 were reported in Ireland on Monday.
The latest figures show that 461 Covid-19 patients are in hospital, 91 of whom are in intensive care.
The overall positivity rate, among all swabs taken, was nearly 50%.
Health officials believe that 87% of reported cases in Ireland are now due to the Omicron variant.
The Department of Health tweeted that it was anticipating “large volumes of case numbers over the coming period”.
Earlier HSE chief executive Paul Reid tweeted: “Well done to all of our vaccination teams. Back at it.
“It’s never too late to receive your 1st dose vaccine. And please take the earliest opportunity to receive your booster.”
Ireland already has a range of restrictions in place, amid concerns about the spread of the Omicron variant.
All restaurants, bars and cafes have had to shut their doors at 8pm.
Indoor events have a limited attendance to 50% of capacity or 1,000 people, whichever is lower.
Outdoor events are also limited to half capacity, to a maximum of 5,000 people.