Coronavirus is now spreading in "quite a significant number of counties", public health officials have warned.
NPHET is raising particular concerns about the situation in Donegal and Louth, but also are also noting increases in Cork, Kildare, Offaly, Wicklow and Waterford.
Health officials say their current best estimate for the virus reproductive number - based on last week's data - is between 1.5 and 1.7, a number said to be "far too high".
Today saw 234 new confirmed cases - including 103 in Dublin and 30 in Donegal.
At this evening's press conference, officials urged people right across the country to pay attention to advice about reducing social contacts.
Less than a week after new restrictions were announced for Dublin, NPHET modeller Prof Philip Nolan said the virus is now spreading in many parts of the country.
He said: "[We've a] particular eye on Donegal and Louth, but not just those counties: Kildare, Offaly, Wicklow, Waterford and Cork each have quite different problems.
"There's a clear signal here to people right across the country, to pay careful attention to public health advice - even if they're not subject to particular restrictions.
"The objective remains - as it did last week - that both the restrictions and advice are designed to bring the reproduction rate below one. That's the only sustainable position to be in."
'It will be another county tomorrow'
Acting Chief Medical Officer Dr Ronan Glynn, meanwhile, said one in three cases in Donegal are in people aged 15-24 years of age.
He also noted public health officials are seeing a large number of family and extended family outbreaks.
He said: "It's Donegal today, it will be another county tomorrow, and another county the day after. I would implore people to not wait until they hear a warning from this table, and cut their social contacts now."
Dr Glynn said he understands this is a very difficult time for the country.
He said: "Everybody is sick and tired of this at this stage - the idea of having to face into restrictions, measures, decreasing our social contacts is frankly a horrible one for people.
"Unfortunately that's the situation we find ourselves in in Ireland - it's the situation countries find themselves in across Europe.
"It is vital that over the coming days and weeks that people reduce their social contacts."
He said the northern parts of Wicklow and eastern side of Kildare are other areas of concern.
However, he said there has been an improvement in the situation in Limerick, Tipperary and Leitrim - saying that happened because people responded to the advice.