Over 5,000 HSE staff are out of work due to Covid-19, leading to a mass cancellation of appointments for patients.
Chief Operations Officer Anne O'Connor warned that overcrowding is also a major problem for Irish hospitals, with extremely high numbers attending emergency departments nationwide.
On Tuesday, the HSE updated its latest Covid case tally count to show that there have been close to 90,000 new cases since St Patrick’s Day.
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It announced 63,954 cases on Monday for the five-day period March 17 to March 21. There were also 23,702 new infections confirmed for the previous 24 hour period.
Ms O'Connor said: "Hospitals are under significant pressure and community services are as well.
"This isn't just hospitals, we have nursing homes under serious pressure with 60% of all older persons services now working without breaks.
"We have our mental health services and our disability services under pressure, it's across the board.
"The thing that's really hitting us again is staff absences. As of yesterday (Wednesday), we had over 5,200 people now out on Covid leave.
"What that means in real terms for people listening is that if you go for example to Limerick - they had serious problems with some of their specialties, where you have a consultant and their team out with Covid.
"If that's a speciality like EMT, or endocrinology, where you might only have one consultant in a hospital - if they're gone and their team is gone, we can't provide that service at all."
Ms O'Connor noted that University Hospital Limerick in particular is facing problems - saying that the hospital "bucked the trend" by never seeing a drop off in patients in the emergency department.
"What is a very real concern for us today is whole teams of staff being out. This is a huge risk for us this week because of the high number of people in hospital," she told RTE's Morning Ireland.
"We had a meeting yesterday, many of the sites have cancelled procedures already. We have always tried to maintain the critical works where they really need to come in. But it is clear to us that our hospitals cannot continue to do a lot of planned elective work. We'll be writing to hospitals to say that we support the cancellations for another couple of weeks, because it is really important that our hospitals are as safe as they can be.
"None of us want to cancel procedures, it's a last resort for us. We will do everything we can to keep the urgent procedures going for people who have very serious conditions and need operations etc.
"In the last month, we have had unprecedented numbers attending A and E and then the staff absences. Unfortunately that (cancelling procedures) is where it brings us. Whether it's in our hospitals, national ambulance service, our community - we are really struggling with the level of Covid across the services and across our staff."
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