The Taoiseach says everyone, including children, will be asked not to socialise as much as planned over the next two weeks.
Public health officials are warning there's a high incidence of Covid-19 among 5 to 11 year olds and their parents.
New guidelines are also being considered that would see children from third class up wearing masks in school, on public transport and in shops.
Speaking on his way into Cabinet, Taoiseach Michael Martin said society needs to cut back on socialising.
"The key evidence from the public health doctors yesterday is that there is a very high incidence of Covid amongst 5-11 year olds and their parents. This is what is concerning public health doctors.
"Hence, they are saying for the next two weeks to reduce the level of socialisation across society, and in particular inter-household mixing."
The Health Minister has promised to bring clarity to parents over how they should keep their child safe from Covid.
Speaking on his way into Cabinet, Stephen Donnelly said the measures are needed as case numbers are growing among primary school children.
"The analysis that we saw last night shows that it is particularly high in 9,10 and 11 year olds, and hence the recommendation of masks from third class up.
"The evidence we have suggests that they have been really effective in secondary schools, so we'll be discussing that this morning."
