Three people with Covid-19 have died, according to the Health Protection Surveillance Centre.
There have now been 1,738 Covid-19 related deaths in Ireland.
Six more confirmed cases of Covid-19 have been reported, bringing the total number of cases to 25,477.
The HSE is working to identify any contacts the patients may have had to provide them with information and advice to prevent further spread.
"The National Public Health Emergency Team continues to advise against all non-essential travel," said Dr Tony Holohan, Chief Medical Officer, Department of Health.
The WHO has warned that the global pandemic is accelerating. In the past week, over 160,000 cases have been reported each day.
“The National Public Health Emergency Team will meet again tomorrow as it continues to monitor the spread of Covid-19 nationally and internationally, and review Ireland’s response and preparedness to the disease.”
Dr Ronan Glynn, Deputy Chief Medical Officer, said 31 cases of Covid-19 in Ireland last month were associated with travel.
"The balance of keeping the disease suppressed in Ireland will continue to be challenging as society and business reopens," he said.
Meanwhile, there have been no further coronavirus linked deaths reported in Northern Ireland, with the toll recorded by the Department of Health remaining at 551.
There was one new case of the virus confirmed there, bringing the total in the region to 5,761.