Testing of close contacts of confirmed Covid-19 cases is to resume on Friday, the HSE said.
At the end of December testing of close contacts was suspended temporarily to prioritise testing of symptomatic cases.
It was a result of pressure on the testing system due to widespread community transmission seen in the third wave.
HSE chief executive Paul Reid said:
Mr Reid said there had been a "modest decline" in the number of people in hospitals with the virus, but said the health care system will not see the benefits of this "for some time to come".
The number of hospital staff absent from work as a result of being a Covid positive case, or a close contact of a positive case, has also reduced.
Mr Reid said: "It's still at a high level of 5,500, but down from 6,600 last week."
Capacity in intensive care units "remains to close to a tipping point for us to have any level of comfort", Mr Reid said.
There are 1,620 Covid patients in the hospital system currently and 216 of those are in ICU as of Thursday lunchtime.
There are 330 patients in ICU overall, including non-Covid patients, leaving just 18 intensive care beds free across the country.
There have been over 800 deaths linked to coronavirus in January alone, Mr Reid said.
In response to news that German public health officials have advised that the AstraZeneca vaccine not be administered to the over 65s population, the HSE said it will wait for the advice of the European Medicines Agency, which is anticipated on Friday.
Ireland has administered a total of 161,500 vaccines to date, the HSE has said.
As of January 27, 71,600 doses have been administered to long-term residents and staff in care facilities.
A further 89,900 were given to frontline health care workers.
Earlier on Thursday, the Dail heard that Ireland's Covid-19 vaccination programme is likely to miss its target of inoculating 700,000 people by the end of March.