The chief medical officer says a "worrying trend" of new clusters of Covid-19 is developing in Ireland.
The Health Protection Surveillance Centre has today been informed of three confirmed cases of COVID-19.
The death toll there stands at 1,735, with a total of 25,439 confirmed cases, its Department of Health says.
Meanwhile, the United Kingdom announced on Monday that 25 more people had died in relation to Covid-19, taking its death toll to 43,575.
Donegal 464 (0) Clare 369 (0) Kilkenny 355 (+1) Roscommon 345 (0) Kerry 310 (0) Longford 286 (+1) Laois 265 (0) Wexford 217 (0) Carlow 175 (0) Waterford 157 (+1) Sligo 128 (+3) Leitrim 78 (0) #Covid_19 (first time since Friday cases by county provided).
There have now been 5,751 confirmed cases of the virus reported in Northern Ireland since the outbreak.
The last death occurred between May 8 and May 15 with the total number of deaths staying at 27 between May 15 - June 12.
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However, a disease expert in China announced the latest outbreak of coronavirus cases in Beijing had been brought under control. Initial jobless claims declined slightly last week to a still-bruising 1.51 million, according to the Labor Department.
Dr. Ronan Gynn, the Deputy Chief Medical Officer, says that the risk of new cases coming overseas is still important to avoid unnecessary travel.
Dr Holohan said: "As restrictions are lifted and people move about more, it is important that we use the tools that have helped us suppress the virus to date".
"I can not emphasise enough how important it is to remain informed, keep a two-metre distance from others and follow the public health advice on hand washing, cough and sneeze hygiene, and wearing face coverings". The risk of imported cases remains high.
For the third consecutive day, there are no Covid-19 patients in ICU in Northern Ireland.
With the majority of countries only able to test people who are symptomatic, there are fears the total number of people who have contracted Covid-19 is far higher than 10 million.
The chief medical officer has said he is deeply anxious at the prospect of greater foreign travel associated with easing restrictions next month.
"It is essential that we all continue to wash our hands, practice good cough and sneeze hygiene and practice social distance".