Eight more people with COVID-19 have died in the Republic, bringing the total number of deaths here to 1,658.
Ten new cases of the virus have also been confirmed, bringing the total number of cases here to 25,066.
Data from the Health Protection Surveillance Centre has shown that of the 25,056 cases reported to it as of midnight on May 31, 3,292 have been hospitalised and of these, 408 have been admitted to ICU.
Some 7,986 cases are associated with healthcare workers, which is almost one-third of all cases.
"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," commented the Department of Health's chief medical officer, Dr Tony Holohan.
He added that the National Public Health Emergency Team (NPHET), of which he is chair, will meet on Thursday to submit further recommendations to the Government for consideration in relation to phase 2 of the Government's plan to reopen society and business.
Phase 2 is due to come into effect next Monday (June 8).
Meanwhile, according to Dr Cillian De Gascun, director of the National Virus Reference Laboratory, as of midnight on June 1, 348,416 tests for the virus 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%," he noted.
The department's deputy chief medical officer, Dr Ronan Glynn, also highlighted that 47% of people are taking longer than four days from the onset of their symptoms, to being tested.
"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," he said.
Phase 1 of the Government's Roadmap for Reopening Society and Business is now in place. For more information on this, click here.
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