Some 4,000 staff and residents in long-term residential care settings in the Republic have been tested for Covid-19 in the last 24 hours amid ongoing concern about infection clusters.
Health Service Executive (HSE) chief executive Paul Reid said 2,000 tests were completed on Saturday, with the rest carried out on Sunday.
A survey of mortality rates among residents in care facilities, which include nursing homes and mental health and disability services, is also being conducted this weekend to give health authorities a fuller picture of the impact of Covid-19.
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There are 575 nursing homes, including private and public facilities, across Ireland.
At the end of April, 248 residential homes had confirmed or suspected outbreaks of Covid-19.
Dr Colm Henry, chief clinical officer at the HSE, said: "In the first instance, as we've seen in some of the cases during the week, the residents are in a particularly vulnerable setting.
"This virus is highly transmissible and it carries a particularly high morbidity and mortality among older, frailer people.
"Secondly, the presentation in such people is sometimes unusual. Some typical in terms of fever or cough or respiratory symptoms, it can also present with somebody not eating properly, or reduced mobility. Those who are already immobile are extremely frail - the signs are so subtle it's undetectable."
During an HSE briefing on Sunday, Mr Reid said the backlog of testing in Ireland has been cleared.
There are 26 laboratories in Ireland and one in Germany carrying out tests for the HSE. Mr Reid said 60% of the total volume of completed tests are being done in Ireland.
He also warned that the supply of personal protective equipment (PPE) remains challenging.
China has placed stronger controls on the export of its PPE, which he said has the "potential to threaten some of our supply line".
But he added: "We are in a much stronger position than many countries, particularly many countries in Europe.
"It still remains to be a key focus for us so that we keep our staff, and we keep our care workers, and we keep patients and the public safe.
"Therefore, we continue to urge all healthcare workers to be extremely prudent in the use PPE and ensure it is for the correct purposes.
"We are now aiming to accelerate further deliveries that would have been planned much further out into May and June.
"We're working with the Chinese suppliers to see how fast they can accelerate those supplies, and that will be an order of about 130 million euro, over four times the size and scale of the order that we had on the first delivery.
"In that will be a line of gowns and overalls, about 11 million supplies and seven million gloves, two-and-a-half million face shields, six million respirator masks, 10 million surgical masks."
Meanwhile, a respiratory doctor at a Dublin hospital has made a public appeal for donations of protective gowns.
Anne Marie McLaughlin, who works at St James's Hospital, posted a video online in which she thanked people who have already donated PPE and said health staff are "extremely grateful".
But she added they have "one more request".
She said: "In particular we are looking for gowns that our healthcare workers can wear when visiting patients.
"These gowns are long-sleeve gowns, and they are made of material which is impermeable to liquids.
"You can contact us through our email ppeforfrontlinegmail.com."
Elsewhere, Health Minister Simon Harris said he would like to see schools reopen for one day a week before the end of term this summer.
He said the move would provide "breathing space for families", and help the mental health of children and parents.
Speaking to Sunday Independent, he said: "I'd like to see a situation where you could expand somewhat the areas in which people can go beyond their home.
"I am conscience that cocooning may remain a reality for quite a period of time, but is there a safe way that they can get out every now and then and take a walk, but I am not going to be making these decisions."
On Saturday, the death toll linked to coronavirus increased by 41 in Ireland, bringing the total to 571.
The Department of Health also reported 778 newly-confirmed cases, bringing the total number since the outbreak began to 14,758.
