At least 3,530 people have had their first vaccine shot against coronavirus in the last week, with clinics to be extended nationwide this week.
It comes after 2,000 health workers were vaccinated in Cork city hospitals in the last three days alone.
Some 500 more doses of the Pfizer-BioNTech vaccines are to be delivered to Dublin's Beaumont Hospital on Monday.
Some 490 patients and staff were vaccinated there over three days up to New Year's Eve, and the vaccine clinic will begin work again there on Monday afternoon.
At University Hospital Galway, 540 people have received the vaccine.
And all 500 doses issued to Cork University Hospital were used up, before medics started work again there on New Year's Day.
It was one of three hospitals in Cork - along with the Mercy, and the South Infirmary - which got 2,000 more doses to split.
Staff worked through the bank holiday and the weekend to vaccinate their colleagues, bringing the total number in the city who have been given their first dose to 2,500.
All seven HSE hospital groups will receive vaccine shipments this week.
The Government has said the aim is to give 50,000 frontline healthcare staff both doses by the middle of February.
While a spokesperson for the Health Minister Stephen Donnelly has said it is the Government's hope that by autumn, the Irish population will be vaccinated.
It comes as another record 4,962 new cases of COVID-19 were confirmed here on Sunday.
Seven further deaths associated with the virus were also reported in the past 24 hours.
The latest figures bring the total amount of cases here to 101,887, while the number of coronavirus-related deaths stands at 2,259.