The vaccination programme is set to slow down in July as it moves into younger age cohorts, with only two types of vaccine available.
More than 300,000 jabs are being administered each week, but this is likely to drop to 200,000 in July, with only two supply lines available, Moderna and Pfizer.
Those vaccines are the only ones available to younger age cohorts, under advice from the National Immunisation Advisory Committee (NIAC).
The Government had previously set a target of 450,000 doses a week by mid-June, contingent on supply.
HSE chief executive Paul Reid said: “Based on confirmed supply levels to date, our vaccination programme reaches a very strong peak throughout this week and over the next couple of weeks.
“Then in July, we revert to a supply line of two mRNA vaccines, and so supply lines drop again in July.
“Certainly this week and next week primarily will be our busiest and highest peak weeks of the campaign to date.”
He added: “The Pfizer supply drops down, but we no longer have usage for the AstraZeneca or Janssen (which is owned by Johnson & Johnson) vaccines, as we’re moving down below the age in which NIAC have recommended their use.
“So that combination means it’s not the same supply line that we’ve had for this level.
“It’s more graduated back to where it was, but there’s still reasonably strong lines from two suppliers so July will still be a good month, it will still be a strong month.”
From Sunday, people in their 30s can begin registering for their vaccine, but this age cohort is likely to take longer than previous ones.
“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,” Mr Reid said.
There are about 710,000 people in the 30 to 39 age cohort, about 380,000 aged 35 to 39, and roughly 310,000 aged 30 to 34.
An HSE briefing on Thursday heard it will take about three to four weeks to complete the 35 to 39 age cohort.
About 61% of people in Ireland have had their first vaccine dose and 31% are fully vaccinated, Mr Reid has said.
More than 3.4 million jabs have been administered, including more than 2.3 million first doses and 1.2 million second doses.
Ireland has one of the strongest vaccination uptake rates in the EU.
There is about 100% take-up among people over 80, 97% among the over-70s, 92% among people aged 60 to 69, and 87% among those aged 50 to 59.
Chief clinical officer Dr Colm Henry told the briefing that the 14-day incidence rate has now fallen below 100 cases per 100,000 people for the first time since late summer 2020.
“It’s a significant drop and one that reflects the overall trend, and the real impact of the vaccination programme,” he said.
Only 2% of cases are now in people over the age of 65, Dr Henry said, with the vast majority now in people under the age of 45, a predominantly unvaccinated cohort.
There are now 180 confirmed cases of the Delta variant, first identified in India, in Ireland, but it is “inevitable” that those figures will increase, Dr Henry said.
He noted that Covid-19 cases in Britain are doubling every 11 days, with the number of people being admitted to hospital there on the rise since the beginning of June.
Dr Henry said: “We have today 180 cases here, a small proportion of the sequence cases.
“The efforts of everyone to date, even with the reopening of society, have been to stunt the introduction and the spread of this variant.
“But given its behaviour in England and Wales it is inevitable that those figures will go up. That’s what we expect to see.”
He added: “If you’re not vaccinated and you haven’t had a prior Covid-19 infection, you’re very vulnerable to a Delta variant infection, because it’s very contagious.
“It’s infectious, it’s easy to catch it and it may make you sicker than the previous variant.”
However, people with two vaccine doses have “great protection” from the Delta variant, Dr Henry said.