Health Minister Simon Harris says he is nowhere near satisfied with the public's social distancing efforts.
He told Pat Kenny the increase in coronavirus cases here is largely due to the fact that we are doing more testing.
"We very much expect to see a very significant increase in the number of cases of the coronavirus diagnosed in Ireland.
"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've 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."
"But I really have to say this morning: we need people take this social distancing much more seriously... we need people to stay away from each other."
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He says people should keep a distance of two metres from other people.
"But this is one I, quite frankly, just don't think people are taking seriously enough right now - and I really need people to redouble their efforts on that".
"The best chance we have of ensuring our health service can cope... is to make sure we don't have a massive peak in illness all at one time".
"We're preparing for the worst case scenario - that's the prudent thing for any health service to do in a global pandemic."
But he says they hope to protect vulnerable and older people, so they can avoid hospital admission.
He also praised the "incredible response" to HSE On Call for Ireland campaign.
Over 40,000 applications have been made to the initiative.
The group has been asking all healthcare professionals from all disciplines, who are not already working in the public health service, to register.
Mr Harris says Ireland will continue testing as many people as possible, in line with World Health Organisation (WHO) guidelines.
And the HSE is also placing an order for 300 new ventilators, as part of a commercial agreement which is due to be reached shortly.