Outbreaks of the coronavirus in long-term residential settings, including nursing homes, are coming under control with the number in the 'red zone' down to 56.
The 'red zone' signals that the centre is an ongoing source of concern and in need of substantial extra supports.
Anne O'Connor, HSE chief operations officer, said that, of the 520 centres, around 417 are now deemed to be stable.
There are confirmed cases of the virus in 371 homes, but many are coping well.
"That gives a level of assurance that things have actually improved in relation to the residential care for older people," Ms O'Connor said.
"There has been a significant increase in the number of home care staff who have now transferred to doing shifts in nursing homes and 146 of these workers have taken up duty."
It comes as twelve more deaths from Covid-19 were confirmed yesterday, bringing the total number of deaths from the virus here to 1,458.
There were 236 new cases announced yesterday, bringing to 22,996 the total number of confirmed cases of COVID-19 in Ireland.
Asked what the HSE would do differently if there was a second wave of the virus, Dr Colm Henry, HSE chief clinical officer, said they would know much more about how the virus manifests itself in older people.
"It's a new virus and so much has been learned about it, but there is still so much unknown," he said.
He said it was now clear that many older people do not have the obvious classic symptoms of the virus and instead are atypical, making it difficult to spot the infection.
Looking back, there is a lesson for Ireland and other European countries that congregated settings, where frail older people are accommodated together, is not conducive to managing the spread of the virus, he added.
HSE chief Paul Reid said outbreaks in care homes have been a feature throughout Europe and not just in Ireland.
Ms O'Connor said that there are 1,285 disability centres and 315 have had confirmed or suspected outbreaks.
Testing of residents and staff will also be completed in mental health facilities this week, she said.
Meanwhile, the Education Minister has said it is too early to say how schools will reopen fully in September due to the need for social distancing.
Schools and colleges have been shut since March in a bid to slow the spread of coronavirus.
Joe McHugh told RTE's The Week In Politics programme he has set up an advisory group to work towards opening schools.
"NPHET advice is that schools will reopen in September, so the question is how can we do that in a safe way," he said.
Asked if schools reopening would mean smaller classes or start times being staggered, he said: "The last thing I want to be doing in the month of May is to say exactly what this will look like.
"That is why I want to have a proper consultation about it."