A total of 33 cases of Covid-19 have now been confirmed on the island of Ireland.
In the Republic of Ireland, two new cases were confirmed on Sunday evening bringing the total to 21.
In Northern Ireland, the Department of Health confirmed that its latest tests had identified five new cases, bringing the total there to 12.
The new cases in the Republic involve a male in a hospital in the south of the country and a female in the east of the country, who has an underlying illness and is seriously ill.
Both cases are community transmissions and not cases involving people who returned recently from at-risk areas.
The man being treated for coronavirus at the Bon Secours private hospital in Cork was admitted for treatment of suspected pneumonia.
He was subsequently transferred to the hospital's intensive care unit, where he has been treated in isolation in a single bed room for a period of time.
Two members of staff at the Bon Secours hospital are self-isolating. They are being tested on an ongoing basis and tests so far have been negative.
Earlier, the Health Service Executive said that it cannot dispute projections that 1.9 million people in the Republic of Ireland may fall ill with coronavirus.
But it said that the modelling scenario is not completed yet.
The vast majority of Covid-19 cases are mild and people make a full recovery. The risk of catching coronavirus in Ireland is still low to moderate, according to the HSE.
It comes after health officials said that the trends in Italy point towards large numbers of cases.
As first revealed by the Business Post, senior health officials believe up to 1.9 million people in Ireland could be infected and become sick.
Around 80% of cases of Covid-19 are a mild to moderate illness, close to 14% have severe disease and around 6% are critical.
The latest data from the World Health Organization is that Covid-19 has an estimated global mortality rate of 3.4%.
Generally, you need to be 15 minutes or more in the vicinity of an infected person, within 1-2 metres, to be considered at-risk or a close contact.
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Minister for Health Simon Harris has said it was highly likely we will see many cases of Covid-19 in Ireland.
He urged people to help slow down the spread of the virus by practising good hand hygiene and taking the advice issued.
The Cabinet sub-Committee on the issue will meet on Monday morning.
On the call for a government of national unity, Mr Harris said there was a functioning Government in place.
But he said Ireland could be dealing with the Covid-19 issue for many months.
Mr Harris said it was above his pay grade to direct party leaders in regard to a government of national unity, but he said that Ireland will need a new government.
DFA advises Irish citizens not to travel to Italian areas
Irish citizens are being advised not to travel to certain areas of northern Italy as significant parts of the country have gone into lockdown to try to stop the spread of the coronavirus.
The Department of Foreign Affairs has advised against travel to the region of Lombardy and to 14 other provinces that have been placed in isolation.
It is also advising against non-essential travel to the regions of Emilia-Romagna, Veneto, Piedmont, and Le Marche where there have been outbreaks of Covid-19.
Milan and Venice are among the cities under the containment order.
Speaking on RTÉ's This Week programme, Chief Executive of the HSE Paul Reid said that modelling work was expected to be completed next week and they will have a clearer picture then.
He said: "That piece of work is being led by the National Public Health Emergency Team and is still in progress."
Mr Reid said part of that evidence is coming from China, Italy, France, the UK and other areas that have been exposed to outbreaks of the coronavirus.
It is also reliant on information from the European Centre for Disease Prevention and Control and the World Health Organization.
He went on to say that the important thing for people to do now is to carry on with a "cleaniness and coughing etiquette" while we are in the containment phase.
Mr Reid said "no short steps" will be taken by the HSE to deal with the virus and he said every acute hospital has a plan in place and along with that they are looking at all the high dependency units.
He described the virus as "unprecedented territory" because it is novel and also in terms of the scale and level of attack and the actions they have had to take.
Separately, 175 healthcare staff from two hospitals are now in self-isolation.
The head of the HSE said that Covid-19 is having a very significant impact, but the safety of healthcare workers, staff and patients is "at the top of everything we do".
Paul Reid said that 100 healthcare workers from Cork University Hospital and a further 75 staff from University Hospital Limerick are involved.
He said the HSE is "taking the appropriate actions that are clinically advised in terms of how and when we can return staff to work quicker and equally how we can regularly medically assess staff in our hospitals".
Professor Sam McConkey has said the coronavirus outbreak here requires a "mobilisation" of Government to respond to it effectively.
Also speaking on This Week, he said it will impact on every Government department, every private industry and every citizen "in a very radical way".
He said he believes there needs to be a re-allocation of around 5,000 public health workers to help out with contact tracing.
He said that is what happened in Wuhan in China and "that is how they controlled it". He said social distancing is also needed and there needs to be more focus on this.
Professor McConkey said a cross-party approach in government is needed to lead us out of this crisis.
Tarik Jasarevic of the World Health Organization echoed this view, saying no government in the world can battle this virus by solely relying on the Ministry of Health.
"It has to be done as an all government approach."
Meanwhile, Dr Chris Luke has said that the projected figures reported do not surprise him, because he says the "epidemiology is basically a matter of mathematics and a matter of mapping the spread of the virus".
Dr Luke, who is a consultant in emergency medicine and a senior lecturer in public health at University College Cork, said that Ireland only currently has around 250 intensive care beds.
He said we "probably don't" have the capacity to deal with an increased demand on intensive care facilities, if the numbers are stark.
"We will have to triage accordingly and be creative in our use of intensive care unit facilities, but very hard decisions may have to be made about who gets intensive care and in what order of priority, so there will be tricky decisions ahead of us", he said.
Additional reporting Paschal Sheehy, Laura Hogan