The emergency measures which have led to school closures and social distancing rules are expected to be extended well beyond this week as health experts meet today to review the coronavirus crisis.
Further restrictions on public places aimed at preventing breaches of social distancing are also expected.
The National Public Health Emergency Team overseeing the crisis will meet today to consider whether to extend the emergency measures, including school closures beyond the original target date of March 29.
The measures are designed to slow the spread of the virus and allow health services to cope with the expected surge in cases.
"I would not be giving anyone any indication that by March 29 we see things changing," said chief medical officer Dr Tony Holohan.
The more successful restrictive measures are in slowing the spread of the virus - the "more likely they are to last longer", he added.
The group will also consider recommendations on how outdoor sites will be better policed to ensure visitors practise social distancing and there is no repeat of crowds flouting distancing rules
Wicklow County Council yesterday closed all council playgrounds, as well as the cliff walk from Bray to Greystones and public toilets on the Bray seafront.
"Wicklow County Council regrets taking this decision and urges the public to follow social distancing guidelines," it said.
It follows the closure of car parks and facilities at Glendalough, as well as both sides of the Sally Gap at the weekend, due to what gardai called "the sheer volume of traffic in the area".
Local communities have expressed fears that crowds flocking to parks, beaches and trails are making it impossible to maintain social distancing
The HSE's tips for social distancing include recommendations to "avoid crowded places", "reduce interactions" and "keep a space of two metres between you and other people".
Health Minister Simon Harris has warned that some public areas may be shut, and said Wicklow County Council was right to restrict car parking and food outlets in Glendalough at the weekend.
However, the minister has also noted the importance of exercise and the outdoors to mental health and well-being as Irish people come to terms with life without schools and sports.
Taoiseach Leo Varadkar said that people visiting crowded parks at the weekend "probably turned up not realising how bad they were going to be so I don't think we should be berating people about this".
"If [the National Public Health Emergency Team] recommends further restrictions, we will implement those further restrictions," he added.
"But any decision was made on further restrictions isn't going to be made because of what's trending on Twitter, or because of populism or political pressure.
"It will be made on the advice of the chief medical officer, and his team of expert public health doctors and biologists, immunologists, and that's as it should be."
Meanwhile, Dr Holohan said that tens of thousands of people are ringing GPs daily seeking tests, but a proportion of these are the worried well.
The HSE has promised that inroads will be made into the backlog of 40,000 people waiting days for a test this week as more than 40 testing centres open around the country today.
The median age of those affected here is 44, which is lower than in the UK and Italy.
Healthcare workers accounted for one in four people infected here.