Over 70s and the medically vulnerable are being asked to cut their contacts to a "very small core group".
The request, from the acting Chief Medical Officer, comes as 613 new cases of coronavirus were reported here yesterday - the highest since mid-April.
Dr Ronan Glynn said health officials are now noticing a "significant escalation" in the COVID-19 situation in Ireland.
He said: "For those aged 70+ and those who are medically vulnerable to COVID-19, it is strongly recommended that you should limit the number of people you meet to a very small core group of family members, carers or friends, for short periods of time, while remaining physically distant."
Anthony Staines, Professor of Health Systems at DCU, believes it will not be feasible for many older and vulnerable people to cut their contacts.
He said: "That's a very large part of the whole population.
"I understand [Dr Glynn's] advice, and it is sound - but it is not a solution.
"What we're seeing happening is the case rates rose in younger age groups, and have now started rising in older age groups - because there's a leakage of cases from the younger age groups to the older age groups."
Professor Staines said many older people also live in 'multi-generational' households with younger relatives, where they can't shield effectively.
