12,000 people aged over 85 will receive a vaccine next week.
The HSE is to start vaccinating people over the age of 70, starting with over 85s, from Monday.
It is aiming to give all 72,500 over 85-year-olds in Ireland their first dose within the next three weeks.
All over 70s are scheduled to be fully vaccinated by mid-May.
HSE chief executive Paul Reid says there are three ways over 70s will be able to get a vaccine.
Mr Reid said: “The vast majority will be done through GP practices, the second element will be three vaccination centres across the country — Dublin, Cork and Galway — and then GP practices will 'buddy up' together, that's all specifically for the 70+ cohort.”
People aged 70 and over should have received both doses of their Covid-19 vaccine by mid-May, the Health Minister has said.
Stephen Donnelly said that despite disruptions to the supply chain, and changing delivery schedules, it should still be possible to vaccinate the entire population by September as planned.
But he warned that this projection is based on “highly conditional forecasts”.