Chief Medical Officer Dr Tony Holohan has called for a redoubling of efforts in the wearing of face coverings in retail settings and on public transport.
Dr Holohan said he would like to see a higher level of compliance in relation to the wearing of face masks or coverings in instances where it it can be difficult to maintain social distance.
Speaking on RTÉ's Morning Ireland, he praised the "fanastic efforts" of the Irish people in complying with the public health guidance to date, but said the message has not got through about the importance of wearing a face covering in certain settings.
He said a television and radio advertising campaign is set to get under way to highlight the importance of wearing face coverings where social distancing is difficult.
It will also advise people about the washing and ironing of masks to keep them in good condition.
Deputy Chief Medical Officer Dr Ronan Glynn said only around 1 in 4 people are wearing face coverings in the recommended settings like shops and on public transport.
He said this needed to change.
"We are asking people to start wearing them all the time in those settings, accepting that some people cannot wear face coverings. What we don't want is for people to start judging others if they're not wearing them. But we believe that if you can wear a face covering, you should", he said.
Dr Glynn says wearing of coverings is a show of solidarity and a commitment to protect others.
"We do fully accept that the message hasn't got out there as strongly as it should have", he said.
He said that Covid-19 is a new virus and that officials are still learning about it.
He said they have been honest about the fact that evidence is changing and that a few weeks ago, the National Public Health Emergency team felt the evidence had changed enough to give the public advice around wearing face coverings.
"Really it's about making the use of face coverings part of normal practice in Ireland. It's not something that we, culturally are used to doing". he said.
He said doing this will require a whole of society approach, from the public, retailers and other public authorities.
There are no plans to provide them for free to the public and Chief Medical Officer Dr Holohan encouraged people to make them at home.
He stressed that the masks do not offer protection on their own and cough etiquette and hand washing should also continue.
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Dr Holohan said that from the beginning of next week the blanket ban on visitation to nursing homes will be lifted.
He said it was a draconian measure and public health experts were very keen to lift it as soon as possible.
Nursing homes have been advised in advance and are taking measures to ensure the safety of residents and visitors.
Quarantine measures at airports are to remain in place and will be changed when appropriate and safe to do so, he said.
Dr Holohan said he does not see a return to "blanket closures" across society and the economy in the event of a resurgence of the virus at a significant level.
He said he is not anticipating a resurgence and has seen drops in all new cases across hospital admissions and ICUs after four weeks of easing restrictions.
Dr Holohan said Ireland is learning from what is happening internationally and would look pro-actively at what measures need to be taken if the virus re-emerges, but, he said, the scale of infection in the public is lower now than it has been.
Dr Holohan said that in March reproduction levels of the virus were growing quickly but now it has fallen and the measures people taking are contributing to the reduction of infections.
He said the population knows now the importance of hand hygiene and respiratory etiquette.
Covid-19 more challenging than influenza
He urged anyone with 'flu like symptoms not to delay in contacting their GP, as coming forward early makes the chances of picking up any new infections sooner.
He said Covid-19 is more challenging and more infectious than influenza.
Dr Holohan said that it is not realistic to say that the high number of deaths in nursing homes and other care settings could have been prevented as he said that "it is a highly transmissible infection" especially for those aged over 80 and this makes prevention of it challenging.
He said influenza is transmitted in significant numbers in these settings each year and as Covid-19 is virulent and spreads even more easily than influenza, it makes the absolute prevention of the spread of Covid-19 unrealistic.
He said that "we know the measures that are important in slowing down that transmission and we need to continue to offer protection to nursing homes", although the numbers of infections have fallen.
He said that deaths in nursing homes in Ireland are at the lower end of the mortality experience in European countries and a lot of reporting had focussed over-simply on the proportion of deaths in nursing homes.
Dr Holohan said that unlike many other countries Ireland has reported comprehensively on probable deaths and confirmed deaths in hospitals and right across the community.
He said reporting of excess mortality, which was carried out by the Health Information and Quality, through analysis of information RIP.ie, shows that there were 1,000 extra deaths this year over the time period since the beginning of the year, most in March and April.
He said this is less than the number of Covid-19 deaths reported so we have "more than explained" the cases of excess mortality in this country.
He stressed that everyone would "like to have seen it lower", but the mortality rate is to the lower end in comparison to other European countries.
He said Covid-19 particularly affects people over 80 and in nursing home settings and he takes no comfort from that and is not complacent about it. He said comparisons that are being drawn with other countries are too simplistic and being made too early.
He said a detailed report on the handling of the nursing homes has been done and an independent expert group is going to identify further "learnings" that could apply to the nursing home sector.
No return to strict lockdown measures if Covid-19 resurges
Dr Holohan has also said the country knows a lot more about Covid-19 than it did in March and that if there was to be a resurgence of the disease, the same measures would not need to be taken.
Yesterday the Department of Health said eight new cases of the virus were reported, the lowest daily figure since the 11 March. It brings the total number of cases to 25,238.
It also said a further eight people have died following a diagnosis of Covid-19. It brings the overall death toll here to 1,703.
The number of confirmed Covid-19 patients in general hospital beds has dropped substantially since April, from 865 at its peak to 116 this week.
The number of people being admitted to hospital is also down over 90% since April, to an average of three people per day.
Meanwhile, the 'R' number, the rate at which the virus is passed on, has remained consistently under one and has been described as "very stable".
Following yesterday's meeting of the National Public Health Emergency Team (NPHET), Dr Holohan was asked what would happen if there was another surge.
He said as we know a lot more about Covid-19 than we did in March we would not need to use the same "blend" of measures as was used previously.
He said NPHET is going to consider what steps it would take if we found ourselves in that situation.
But, he said, we would not have do to things in the exact same way as before as the population will hopefully be maintaining its high level of compliance with public health advice.
Dr Holohan also said although a resurgence of the disease cannot be ruled out - he hoped that as good public health measures are adhered to Ireland would not find itself in that situation.
Around 80% of cases of Covid-19 will be a mild to moderate illness, close to 14% have severe disease and around 6% are critical.
Generally, you need to be 15 minutes or more in the vicinity of an infected person and within two metres of them, to be considered at-risk, or a close contact.