Minister for Health Simon Harris has warned that further restrictions on movement could come into force if people continue to ignore advice about social distancing.
The National Public Health Emergency Team (NPHET) is meeting on Tuesday to consider whether tougher restrictions are needed.
It follows Wicklow County Council closing the Glendalough car parks and facilities after swarms of people gathered in the popular spot over the weekend. There were also reports of large numbers of people on beaches and at tourist locations around Cork.
NPHET will discuss whether to enforce a clampdown on movement in public spaces including walking trails, beaches and parks.
Speaking about the decision to shut the Glendalough facilities, Mr Harris said: "I am very pleased that the council stepped in there and said we can't properly social distance here so we're shutting down the car park, we're shutting down the premises and that's the sort of decisive action that needs to be taken."
Mr Harris told RTÉ Morning Ireland that a number of people have not been able to follow the two-metre distancing measure.
"Perhaps greater guidance in relation to playgrounds and public spaces could be useful as well, and perhaps greater guidance and support for businesses too," he said.
Mr Harris added: "Tony Holohan, the chief medical officer, will analyse all of these things, he will look at the current restrictions and how well does he think they're working and he will give us a view on that.
"He'll also look at any further measures that we should take.
"What we're trying to do here, though, is make sure we can look after the wellbeing of all our people, their mental health and their ability to get out and have a walk, but that's very different to people going to a crowded park together - that's just not on."
On Sunday, health authorities in Ireland confirmed a fourth patient diagnosed with Covid-19 had died.
The male patient, in the east of the country, had an underlying health condition, the health service said.
The Department of Health said on Sunday there were 121 new cases of the virus.
It brings the total number of confirmed cases of Covid-19 in Ireland to 906.
Mr Harris said he expects a delivery of personal protective equipment for health workers to arrive in Ireland later this week.
It comes after Ireland's top health service official said huge orders have been placed for Covid-19 testing equipment and protective gear for staff.
The massive increase in demand is due to everyone with coronavirus symptoms being asked to self-isolate and await a check.
Almost 40,000 sample test kits are being distributed. Another 20,000 will be in Ireland by Wednesday, the health service said.
Ireland is at an advanced stage of negotiations with China to secure a further 100,000 and good progress is being made, it said.
Mr Harris added: "I can't put a specific day on it, we're hoping to begin to see the arrival of some of this towards the end of the week.
"There is personal protective equipment already in Ireland and what the HSE (Health Service Executive) are trying to do this week is redistribute what we already have.
"We usually spend about 15 million euro on personal protective equipment, we're spending over 200 million this year - huge efforts have been undertaken by the HSE to secure this in what is quite a difficult market.
"There's a worldwide shortage of this, they've done really, really well and I know it can't come quickly enough.
"I know our health care professionals are just doing a brilliant job, and we all want to and we will protect them."