Eight more people have died from COVID-19 in Ireland.
Latest figures also show that there have been 10 new cases of the virus.
This brings the death toll here to 1,658 and a total of 25,066 cases.
The HSE says it is working to identify any contacts the patients may have had to provide them with information and advice to prevent further spread.
Data of all cases, as of midnight on Sunday, reveals:
- 57% are women and 43% are men
- The median age of confirmed cases is 48 years
- 3,292 cases (13%) have been hospitalised
- Of those hospitalised, 408 cases have been admitted to ICU
- 7,986 cases are associated with healthcare workers
Dublin has the highest number of cases at 12,090 (48% of all cases), followed by Cork with 1,517 cases (6%) and then Kildare with 1,419 cases (6%).
Of those for whom transmission status is known community transmission accounts for 39%, close contact is 58% and travel abroad accounts for 2%.
Dr Tony Holohan, Chief Medical Officer, said: "Over the past week there have been approximately 500 new cases of COVID-19 notified, 54% of which are aged between 24-55 years old.
"Incidences of these cases are spread across 21 counties in Ireland.
"While we are doing well, the potential for spread remains present across all regions of the country."
Dr Cillian De Gascun, director of the National Virus Reference Laboratory, said: "As of midnight Monday 1 June, 348,416 tests have been carried out.
"Over the past week, 22,621 tests were carried out and of these 389 were positive, giving a positivity rate of 1.7%.”
Dr Ronan Glynn, Deputy Chief Medical Officer, added: "47% of people are taking longer than four days from onset of symptoms to being swabbed.
"We are strongly encouraging all members of the public to know the symptoms of COVID-19 and seek medical attention as soon as symptoms appear."
NPHET will meet on Thursday to submit further recommendations to Government.
It comes as almost 40,000 people have left the Government's COVID-19 Pandemic Unemployment Payment (PUP) scheme.
The Department of Social Protection has issued payments of €190.2m to 543,200 people - a drop of 36,200 on the number of people paid at the same point last week.
Among them are 28,400 who have told the department they are returning to work - and 20,100 of these will be receiving their last payment this week.
As well as those on the unemployment payment, there are now over 57,800 employers who have registered with the Revenue Commissioners for the Temporary COVID-19 Wage Subsidy Scheme - with at least one subsidy being paid to over 508,100 people.
These payments are in addition to the 214,700 people who were reported on the Live Register as of the end of April.
