137 people have died in the Republic after contracting Covid-19 - including 17 in the past day.
There are now 4,604 people diagnosed with the disease in the country, after an increase of 331 positive tests for coronavirus.
The figure includes 1,084 cases among healthcare workers.
Health Minister Simon Harris says people have to work to try and keep the reproductive rate of the disease low.
He said: "On March 16 if you were infected with Covid-19, you were likely infecting 4.3 other people,
"By the end of March that had dropped to 2.5 other people, but we need to get that number below 1,
"Because if we get that number below 1, it means the virus does not sustain itself in the community,
"It means that every person who gets sick is not replacing themselves....with another person who has the virus."
Yesterday the Minister for Health Minister announced measures to help nursing homes protect themselves from a coronavirus outbreak.
There are 40 clusters – three or more Covid-19 cases at institutions within 72 hours – in nursing homes.
Staff screening will start in nursing homes twice a day, with testing prioritised for staff, and access will be provided to personal protective equipment (PPE), expert advice and training.
