Health Minister Simon Harris said that public health advice on social distancing during the coronavirus outbreak is "not being taken seriously enough", as he noted the number of cases is about to soar.
Yesterday, 126 new cases of Covid-19 were confirmed in Ireland, bringing the total to 683 - a daily increase of 23pc.
Mr Harris said that Irish people have an inflated sense of our reaction to the outbreak and need to take social distancing measures more seriously.
"I wouldn't have a national slap-ourselves-on-the-back campaign in terms of social distancing," he said.
"I know lots of people are making efforts, but I am nowhere near satisfied that we're taking social distancing seriously and if you look at some of our parks -and it's absolutely appropriate for people to go home, get some fresh air, take some exercise, that's actually good for you - but it's not good for you to be in crowded parks.
"It's not good for the teenagers to be getting together. This is not the summer holidays.
"We do need people to take social distancing seriously and what that means is, there should be two metres between you and other people.
"We need people to take this social distancing much more seriously, and maybe when we talk about social distancing, it's a phrase we're not very familiar with.
"We need people to stay away from each other.
"We need people to keep their distance, no matter where you are, you should be trying to stay two metres away from other people.
"I quite frankly just don't think people are taking it seriously enough right now, and I really need people to try and redouble their efforts on us."
Experts warned that up to 15,000 people could be infected in Ireland by the end of the month.
Mr Harris said that he wants to reassure the public, but there will be a "significant increase" in the number of cases in the coming weeks.
"We very much expect to see a very significant increase in the number of cases of the coronavirus diagnosed in Ireland," he said.
"We've gone from a situation whereby until recent days we were only really testing people who'd come back from certain parts of the world - largely Italy and China - to now many GPs referring people for tests on the basis of symptoms.
"So we're gone from a situation of a couple of hundred people a week being tested to a situation where many thousands a day could be tested.
"But the numbers are still a cause for concern, and we know they're going to go up."
Speaking on The Pat Kenny Show, Mr Harris did, however, say that Ireland is in a good position in terms of medical equipment, including 39,000 testing kits arriving in Ireland.
"So far, the ICU rate is about 2pc, so seven people who have been admitted ICU, and so far there's been 31pc of cases hospitalised - but that figure is a bit skewed because up until last Thursday we were hospitalising everybody with the diagnosis," he said.
"On the issue of ventilators, this country has some of the biggest global companies in the world producing ventilators based here in Ireland.
"It would be most bizarre, if not unethical, that you'd have a situation whereby ventilators were being produced in Ireland, and we weren't able to access them here in Ireland.
"The HSE has about 500 already.
"On top of that, we will have 250 ICU beds with ventilation and the private hospitals, which we're in talks with, and talks that need to continue quickly.
"They have 164 ventilation rooms.
"We're about to reach a commercial agreement that we will receive about 300 more ventilators, plus 80 more a week," he added.