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 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," she 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.
Asked what the HSE would do differently if there is a second wave of the virus, Dr Colm Henry, HSE chief clinical officer, said it 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 and there is still so much unknown," he said.
He added it is now clear, and this was not strongly known previously, 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, are not conducive to managing the spread of the virus, he added.
HSE chief executive Paul Reid said outbreaks in care homes have been a feature throughout Europe and not just in Ireland.
Ms O'Connor said 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.
The Citywest Hotel in Dublin remains open to people who want to self-isolate.