The Health Minister Simon Harris says the number of critical coronavirus cases should "worry us all."
Seventeen people lost their lives from the virus on Tuesday, while 325 new cases were confirmed here.
The figures are the highest daily increases so far and means 3,235 people now have the infection in Ireland.
Some 113 people have been admitted to Intensive Care Units with the virus.
Minister Harris told Newstalk Breakfast that is a concerning figure.
He said there is "absolutely no room for complacency."
"Very serious concerns in relation to ICU occupancy, very serious concerns, should worry us all.
"Serious concerns in terms of clusters in nursing homes, worries about the levels of healthcare professionals getting this virus - not just in Ireland, but globally.
"[It's] very early days with a long way to go on this.
"But the efforts you've made through the work on phase one has had an impact.
"What we all have to really hope and work for now is that the measures we put in place on Friday have a further impact.
"And if they do I hope we'll be in a position to try and report progress by Easter Sunday."
Minister Harris also said the HSE has secured "a constant supply" of testing kits as testing centres are continuing to be set up across the country.
He admitted there is a capacity issue at the moment which "is likely to last for about another seven to 10 days."
"We have more capacity coming on stream in terms of our labs in the coming days".
"We're going to continue beefing up our testing capacity in this country, but the most important thing you can do is self-isolate if [you have] any symptoms.
"Priority number one, two and three for me for this week is trying to provide extra supports for people in long-term residential care settings, including nursing homes, and the staff working there".
Mr Harris said measures are to be announced soon to help healthcare staff with childcare.
"We're trying to deal with many things at the same time - we're prioritising first and foremost measures that are going to save people's lives - and then obviously we're also looking at measures we can put in place to tey and support people doing incredible work on the frontlines.
"We are going to come forward with proposals in the coming days - my colleague Katherine Zappone, the minister for children, has been working very intesively on this".
He said he expects measures are likely to be ready by the end of the week.
