Both patients are male and in the east of the country.
The total number of confirmed cases of the disease in Ireland has now reached 1,125 after a further 219 patients tested positive.
The median age of confirmed cases as of midnight on Friday is 44 and 211 people have been hospitalised.
Ireland has so far introduced an emergency 203 euros-a-week payment for employees and self-employed people who have lost their jobs or had hours cut and the government has said it will refund the same amount to struggling firms who keep staff on.
29% of people who have COVID-19 have been hospitalised, and of those cases, 25 have been admitted to ICU.
Of those for whom transmission status is known, community transmission accounts for 45%, close contact accounts for 23% and travel overseas accounts for 31%.
"I would like to acknowledge the efforts of everyone adhering to public health advice". Many more are waiting to be tested and on results within the county.
It expects the backlog to be tackled in the coming days.
35,000 expert testing kits have been available from today and the HSE has confirmed that another 20,000 will arrive next week.
Across Ireland, 50 test centres have been set up.
She said there will be a big expansion in testing centres this week and some 41 centres should be operational by Tuesday with the largest in Pairc Ui Chaoimh in Cork.
Mr Reid said in the coming weeks the public would witness the Health system under stress like we had never known before. You are actively helping flatten the curve and limit the spread of Covid-19. "Public health doctors carrying out contact tracing are advising that confirmed cases are now reporting fewer contacts, which is an encouraging sign that people are following the public health guidance".
The HSE also said 177 patients with coronavirus are now in hospital and 30 are in intensive care, a significant escalation in numbers. Tony Holohan stated that the average waiting time for a test is "longer than we would like".
Ireland has so far put aside 3 billion euros to mainly boost sick pay for workers impacted by the virus, fund the health service and offer assistance to businesses.
84% of people say they are practicing social distance in a queue. All aspects of our public health advice are constantly reviewed by the National Public Health Emergency Team and we will not hesitate to take more measures where necessary, based on epidemiological evidence and in proportion with Ireland's experience of this outbreak.
He said the Chief Medical Office has said that if social distancing works the rate of growth in new cases should begin to slow down by the end of this month or the begininng of April. For the third day in a row, no new confirmed or suspected cases have been reported in Wuhan and in Hubei.