191 new cases of coronavirus have been confirmed in the Republic, while a third patient has died.
The number of cases in the Republic is now 557.
Health officials are now "working rapidly" to identify any contacts the newly-diagnosed patients may have had.
Today's increase compares to 74 new cases confirmed yesterday and comes amid an increase in recent days in the level of COVID-19 testing being carried out across the country.
— Stephen Murphy (@Stephen_Murphy5) March 19, 2020
In an update on the 350 cases reported as of midnight on Tuesday, the Department of Health said there were 26 'clusters' of cases.
31% of those cases were hospitalised, while seven cases (2% of the total) were admitted to ICU.
Community transmission accounted for 35% of the 350 cases, travel for 21%, and local transmission / close contact for 21%. 71 other cases remained under investigation.
84 healthcare workers have been diagnosed with COVID-19 - with almost two-thirds of those cases not linked to foreign travel.
Meanwhile, Monaghan is now the only county in the country to have not reported a case of the virus.
Chief Medical Officer Dr Tony Holohan extended his condolences to the family and friends of the patient who had died.
He also said: "It is too early to see any impact of our social distancing measures.
"This data underscores the importance of younger people to rigorously follow public health advice and social distancing measures."
Nine new cases were confirmed in Northern Ireland today, bringing the total there to 77.
The all-island total now stands at 634.
Officials in the North today also confirmed a COVID-19 patient had died there - the first coronavirus-related death in Northern Ireland.
Meanwhile, Italy has overtaken China as the country with the most coronavirus-related deaths.
427 people died today bringing the total number of fatalities in the country to 3,405.
The death toll in China is currently 3,249, according to data from Johns Hopkins University.
The latest figures from Italy are up to 41,035 from a previous 35,713 - a 14.9% increase, slightly higher than seen in recent days.
However, the number of deaths announced today was down from the 475 deaths yesterday.
China remains the country with the most confirmed cases, with more than 80,000 people diagnosed with COVID-19.
Over 235,000 cases have now been confirmed globally - with China, Italy, Iran and Spain the countries with most confirmed cases to date.