Over 15,000 people across the country have received the first dose of the COVID-19 vaccine.
The HSE says its target is to administer 35,000 doses by the end of this week, and pledged that vaccination is happening seven days a week.
Amid growing hospitalisations from the virus, CEO Paul Reid also said an agreement to use private hospitals is being finalised - and that he expects all of them to sign up urgently.
However, he described the current situation with COVID-19 as quite bleak.
He said: "We're working to deal with an extraordinary national crisis at the moment.
"In the last 24 hours, we've reached a milestone that has to be a call to arms to everybody to support the health service in the coming weeks and months.
"We now have 1,022 people being treated in hospital with COVID - and as of mid-morning there are now 95 people with COVID in ICU."
Earlier, Health Minister Stephen Donnelly defended the speed of the vaccine rollout here - insisting it's 'not slow'.
He said around 40,000 doses of the Pfizer / BioNTech vaccine are set to be administered here weekly, with details being finalised for the arrival of the newly-approved Moderna vaccine.
Minister Donnelly said the only constraint on vaccinations "will be the arrival of vaccines here in Ireland", as officials are moving "as fast as it is possible to move".
