Two more people have died from the coronavirus, a man and a woman in the east of the country.
The number of people who have tested positive for the coronavirus has risen again by 235, bringing the toll to 1,564.
Nine people have died now from the virus in the Republic.
Dr Tony Holohan, chief medical officer, said there are more cases of the virus out there which have not yet been detected.
He emphasised the need for people to self isolate if they develop potential symptoms.
He said the Department of Health had not been informed if the deceased man in the east, whose death was announced today, had an underlying condition.
He said more people than are likely to have the virus have been seeking a test and the criteria had been tightened to make the testing sustainable.
Asked about incidents of people coughing into others faces, he said it might well be that a member of an offender’s family could end up with the virus.
Dr Ronan Glynn, deputy chief medical officer, said Ireland is among the top countries in the world for testing.
But the vast majority who were tested in recent weeks were negative, therefore it was better to target particular groups who are most vulnerable to the disease.
This comes as Health Minister Simon Harris revealed that almost 13 years worth of personal protective equipment (PPE) will start to arrive in Ireland by the end of the week.
"Usually in a year we'd spend about €15 million on personal protective equipment - we're going to spend about €225 million this year," he said.
In an interview with Virgin Media News, Mr Harris said that he was "really pleased" that Ireland, through the HSE, had secured the equipment haul during the global shortage of supplies.
He said that the supply, which is due to start arriving by the end of the week, is "probably what would normally do you for about 13 years."
Speaking about the latest safety measures announced by the Government yesterday, which saw the closure of non-essential retail outlets, the minister said that the public should follow the advice and "take it day by day".
"We will do what we need to do, and we'll do everything we can do - but it will only work if we do it in partnership with the people," he said.
He also urged the public to look at the breakdown of the figures and not just the daily cases, and that "the trend is going in one direction".
"Of course the daily numbers of new cases in Ireland are of interest. It's of interest to me, it's of interest to all of us, on a human level and curiosity level it's of interest.
"It's nowhere near though as important, in my view, as what we're seeing in relation to our ICUs. We are seeing a number of people in our country get very very sick and end up in intensive care.
"There are more people in Ireland today with Covid-19 than yesterday, there will be more tomorrow and today.
"But even more importantly than that we have seen a significant number admitted to ICU, and sadly we've seen several people lose their lives."
Earlier today, Taoiseach Leo Varadkar said Ireland will not now reach the previously estimated 15,000 cases of coronavirus in Ireland by the end of March.
He said: “That was based on a 30 to 33pc increase in new cases every day, that being an exponential increase, that hasn’t happened yet.
“It looks like we’re going to come in certainly lower than 15,000.
“That is of course 15,000 confirmed cases of coronavirus, there are many more cases that are not confirmed.
“I hope that is some evidence of some of the measures that people are taking are having some effect, but what is certainly the case is the number of new cases is continuing to rise.”
He stressed the figures should not be taken as a sign that Ireland is containing the virus.
Elsewhere, new rules have been introduced in Ireland for people seeking testing for coronavirus.
Patients requesting a test will now have to display two major symptoms – a fever and at least one sign of respiratory disease, like a cough or shortness of breath – before they are referred.
People will also have to fall into a particular group to be tested.
This includes those in contact with a confirmed case, healthcare workers, vulnerable groups and those who live in long-term care facilities.
Chief Medical Officer Tony Holohan said: “What’s clear is that the volume of people who are seeking testing has been very large and there has been a very significant increase in the number of people coming forward.
“Over the last 10 days something in the order of 20,000 people a day have sought testing.
“If we were to test at that regime we would, by a considerable distance, become the number one country in the world for testing.”
He said a lot of people requesting tests are not appropriate for it.
He went on: “We needed to think about focusing our case definition to identify people with a higher probability of having this particular infection.”
Around 1,300 tests are being performed in Ireland every day and that is expected to rise to around 3,000 a day by next week, and to around 16,000 daily in the coming weeks.