Five more people with COVID-19 have died in the Republic, bringing the total number of deaths here to 1,664.
Thirty-eight new cases of the virus have also been confirmed, bringing the total number of cases here to 25,142.
Data from the Health Protection Surveillance Centre has shown that of the 25,104 cases reported to it as of midnight on June 2, 3,311 have been hospitalised and of these, 410 have been admitted to ICU.
Some 8,025 cases are associated with healthcare workers, which is almost one-third of all cases.
According to Prof Philip Nolan, chair of the National Public Health Emergency Team (NPHET), the reproductive number of the virus is still estimated to be below one.
"The reproductive number is hard to estimate at the moment because numbers are so low, which is good news, but we are still confident it is well below one, lying somewhere between 0.4 and 0.7," he explained.
According to the Department of Health's chief medical officer and NPHET chair, Dr Tony Holohan, further progress has been made throughout May in suppressing the spread of the virus.
"A downward trend is evident in the number of hospitalisations, ICU admissions and reported deaths. Adherence to public health personal behaviours - hand washing, physical distancing, and cough/sneeze etiquette - is essential in avoiding an upsurge of infection in the future," he added.
Phase 2 of the Government's plan to reopen society and business is due to begin next Monday (June 8). Phase 1 is now in place. For more information on this, click here.
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