Vaccination of people with underlying conditions will start next week, according to the Health Minister.
However, Stephen Donnelly has said he has concerns about the capacity of AstraZeneca to meet delivery targets.
The HSE missed last week's target of 100,000 vaccinations with the Tánaiste saying an under-delivery from AstraZeneca was to blame.
Health Minister Stephen Donnelly says despite that the pace of the roll-out is increasing:
"(It) it really really good and welcome news (that Cohort 4 will begin to be vaccinated). It's a complex group, there's complex work and panning and engagement going on.
"The HSE is currently working through the details for how these patients will be contacted and indeed where they will be vaccinated."
However, HSE chief executive Paul Reid says AstraZeneca supply issues will have an impact on this week's aim of 92 thousand doses.
"We've been advised by AstraZeneca that these commitments will balance themselves out over the three-week period, but we still do continue to have concerns about it because it has been an interrupted and changing supply commitments.
"It has particularly impacted us last week, and will continue to do so this week as well."
