There is increasing concern following confirmation of another 3,680 Covid cases today.
The number of people in hospital who have tested positive for the disease is 543, down eight since yesterday.
There are 97 people being treated in intensive care.
HSE boss Paul Reid said hospitalisations have increased by 20% in the last week and warned that the health system alone cannot find a way out of the current wave of Covid-19.
He told RTÉ’s News at One that “no health system on its own can get its way out of this … and cope with that level of surge and relentlessness at a peak that we are seeing right now”.
Mr Reid said RSV (respiratory syncytial virus) is leading to hospitalisations, while other seasonal viruses are also having an impact, with many emergency departments seeing presentations up 20% on pre-pandemic figures.
He said many attendances are older people impacted by delayed care as a result of the pandemic.
Mr Reid said increased resources have been put in place, with 11,000 extra staff and 900 more hospital beds, but the surge continues to stretch the system.
He said that even the most resourced healthcare systems in Europe are under significant pressure, including in the Netherlands and Germany.
The number of Covid-19 outbreaks in Ireland increased last week, according to the latest figures from the Health Protection Surveillance Centre.
There were 173 outbreaks, an increase of 45 on the previous week.