More than 10 patients have died from Covid-19 in the country's largest public care centre for the elderly, the Irish Independent understands.
There have also been up to 50 cases of the virus recorded at St Mary's Hospital in Dublin's Phoenix Park in recent weeks.
A number of staff members are believed to be among those who have fallen ill since an outbreak took hold.
The HSE confirmed that since April 2, there have been "11 Covid-19-related deaths of residents in St Mary's Hospital, 10 of which are confirmed Covid-19 positive and one which is a suspected case, awaiting result".
"We offer our deepest sympathies to their family and friends and our thoughts are with them at this difficult time," the health authority said in a statement.
St Mary's Hospital, which provides care for older people, has 198 residential places. Care provided ranges from stroke rehabilitation for adults of all ages to residential care for older adults. The HSE said it was in contact with relatives and next of kin of all residents in St Mary's Hospital about any suspect or confirmed cases of Covid-19.
A spokesperson said: "Where a relative has any query relating to the care of a resident, we ask them to contact us directly. The safety and well- being of our residents and staff is our priority. Many of the team working in St Mary's Hospital worked closely with residents over a long period, and we also offer them our sympathies."
The news of another major outbreak in a care facility for older people comes a day after it emerged eight residents in a Co Laois elderly care centre have died from Covid-19 since the weekend.
The tragic deaths in the Maryborough Centre at St Fintan's Hospital in Portlaoise meant more than a third of the care centre's patient died from the virus over the Easter weekend. Those who died from the virus were aged between 66 and 84.
Nine people died in the HSE residential care centre last weekend but eight were confirmed to have contracted Covid-19.
The remaining 17 patients in the psychiatric care centre are being treated as if they have the virus regardless of test results or whether they are showing symptoms.
The Bishop of Kildare and Leighlin, Denis Nulty, said last night the best possible care must be delivered to vulnerable patients and those who die dfrom the Covid-19 were more than statistics.
"The news brings home to us in a very dramatic way the huge need for special care for those who are grouped together in similar centres or in homes for vulnerable or older people," he said.
"It is imperative the best possible treatment is made available to those who are most vulnerable to Covid-19 and that staff working in these homes and facilities are equipped with a sufficient and proper supply of PPE. Every life matters. Every life counts. Every life is precious irrespective of age or potential productivity."
Meanwhile, the National Public Health Emergency Team (Nphet) has denied instructing nursing homes to keep details of Covid-19 cases from the families of residents.
In the Dáil, Fianna Fáil leader Micheál Martin said he had been told of a nursing home that told families it could not give out information on coronavirus cases due to instructions from Nphet.
However, Nphet said: "Communication of clusters and outbreaks are essential to the Department and the HSE. We need to find the virus so we can isolate it and address it."