People have been urged to keep up their "guard and resilience" in the fight against Covid-19 as the health service reported continue signs of encouragement.
HSE chief executive Paul Reid said the number of cases were reducing, and that the positivity rates and the number of close contacts were also declining.
But he stressed that hospital cases and the number of people in intensive care had not yet reduced.
Mr Reid made the comments as 552 new cases of Covid-19 were confirmed by the National Public Health Emergency Team, 86 of them in Cork.
Two more deaths linked to the virus were reported.
As of 2pm on Sunday, there were 330 Covid-19 patients in hospitals, including 47 people in intensive care with the virus.
There have been 17 additional people taken to hospital in the past 24 hours.
Mr Reid appealed to people to keep up their efforts over the coming weeks as the country aims to avoid the trend of rising cases in Europe and the UK.
He tweeted: "Some continued signs of encouragement this week.
"Reducing cases, positivity rates & close contacts.
"But hospital cases & ICU aren't reducing yet.
"So please let's keep our guard & resilience for the coming weeks as we aim to avoid the trend in Europe & the UK."
UK Prime Minister Boris Johnson announced on Saturday that England faces a second lockdown from Thursday until December 2 in a bid to reduce its rising infection rates.
On Saturday Mr Reid said the number of positive cases was continuing to decline, along with reducing positivity & community testing demand.
He said this trend could help reverse the recent growing trend of people being taken to hospital and ICU.
He added: "Not a pleasant time for many but let's keep this early momentum going."
Of the new cases notified to the Department of Health on Sunday, 173 were in Dublin, 86 in Cork, 40 in Limerick, 30 in Donegal and the remaining 223 cases were across all other counties.
Some 63% were under 45 years of age.
The median age was 36 years.
Ireland's 14-day incidence rate per 100,000 population now stands at 253.5.
Cavan remains the county with the highest rate at 590.7, while Leitrim has the lowest rate at 106.1.