The HSE CEO Paul Reid has said while some 600,000 vaccines are to be administered in the next two weeks, this will drop off in July.
But he also said that so far, 3.45 million total doses have been administered.
Some 31% of the adult population is fully vaccinated against the virus, while 61% have received their first dose.
While registration will open for people aged 35 to 39 from this Sunday.
But Mr Reid told The Hard Shoulder the next two weeks will see a further big uptake in vaccinations.
"Very strong rollout right now as we're at - today - 3.45 million total doses administered.
"61% of the population, over 2.3 million, now have received the first dose - and 31% of the population, or 1.2 million, now received their second dose.
"[There's] a good three weeks ahead of us in terms of supply lines and vaccinations.
"This week alone, the week we're in now, we'll have somewhere between 310 and 330,000 vaccines administered.
"And similar for next week again, so strong momentum at the moment".
However he said supply issues will see a drop off in July.
"Those accelerated numbers that we're doing this week and next week are a function of Pfizer being in a position to bring back some of their supply lines which were targeted towards quarter three, bringing them back into quarter two.
"As we go back into July, two things happen: we have the two vaccine supplies...Moderna and Pfizer.
"We won't be able to utilise any further AstraZeneca, with the exception of what we're finishing out in dose twos.
"And indeed Johnson, because we're below the 50-year-olds which are not recommended through the National Immunisation Advisory Committee.
"Our supply lines will revert back to the Pfizer and Moderna supply lines".
But he said July will still be "quite strong".
Second AstraZeneca doses
On people getting AstraZeneca dose two, he said 450,000 people will have received this by the middle of July.
"Originally that was to be done over a nine week timeframe, we're now going to do it over five weeks.
"So between now and the week commencing 19th July, we'll have administered second doses to 450,000.
"People will hear from us, we will make contact through the normal process in text.
"We are putting in extra booths, we are putting in extra vaccination centres to ensure that we vaccinate the AstraZeneca dose twos, along with our continued progeramme of rolling through the ages."
83% of cases 'below the age of 45'
And Mr Reid said the hospitalisation figures show vaccines are bringing the numbers down.
"We now today have 54 positive in-patients in hospital, COVID patients, and 18 in ICU.
"Just think back to the dark days of January, where we had 2,020 people in hospital and we'd 212 people in ICU.
"Even if you look at the cases coming through at the moment - and we do have concerns with the Delta [variant].
"But just if you look at the cases at the moment, 83% of the cases are below the ages of 45.
"Only 6% of the cases are above the age of 55, so vaccines are working".
On suggestions for mixing and matching vaccines, Mr Reid said advice on this has not changed.
"We don't haver any medical guidance or direction from the... National Immunisation Advisory Committee.
"They have not advised on that - on the contrary, they've asked us and directed that we continue with the current [strategy].
"I'm sure they will always assess that evidence, but I would not like to put a mixed message in that there may be a change."
Earlier Mr Reid said vaccinating people in their 30s against COVID-19 will take longer than previous age groups.
He said there were two reasons it will take longer to vaccinate those in their 30s.
"To flag upfront: this will be a slower age group to move through based on volume, but particularly based on the high-level of dose two administrations we will have to do.
"We also move to two supply lines in July - which is Moderna and Pfizer", he added.