The HSE's confirmed just over 15,000 people have received the first dose of a coronavirus vaccine so far.
It's aiming to have 35,000 doses administered by the end of the week.
CEO Paul Reid says the plan is for 135,000 healthcare workers and residents and staff of nursing homes to be vaccinated by the end of February.
R-Number
Meanwhile, the Covid-19 reproduction number could now be higher than 2.
That means for every person who gets the virus, they'll pass it on to at least 2 others on average.
The HSE says positivity rates are reaching 50 per cent in some testing centres - and hospitals are facing an "extreme situation" in the next 10 days.
Chief Clinical Officer Dr Colm Henry says there are signs the UK variant is becoming more of an issue.