The Department of Health has advised anyone displaying symptoms to self-isolate until they can obtain a PCR test. They also asked people to cancel any unwanted tests in order to free up slots.
"We continually monitor the availability of testing appointments across each of our centres and appointments often do become available later in the day," a statement from the Department of Health said.
Christmas Day saw a record number of cases, with 13,765 recorded. This figure was reported despite reduced testing capacity. All of the HSE's 41 test centres are back open from Monday.
To tackle the highly spreading Omicron variant, testing capacity is currently at 35,000 per day, with plans to increase this further.
Chief Medical Officer Dr Tony Holohan has called for anyone displaying symptoms to self-isolate and arrange a PCR test. He has also asked people to avoid crowded places, including shops.
Civil servants are set to decide whether key workers who are close contacts but are asymptomatic should be able to continue to work. There are fears over maintaining public services amid the high infection levels being caused by Omicron.
Departments are "working to ensure the full implementation of existing sectoral guidance, as well as putting in place contingency plans to ensure the continued operation of critical infrastructure and essential services," a government statement said.