The HSE Chief Executive has said it is in a "real race to get the vaccine out ahead of the spread of the Delta variant" of Covid-19.
Paul Reid said it is key that people "take quite serious" the threat of the Delta strain "and treat it with the concern it deserves".
Speaking at the HSE's weekly Covid-19 news briefing, he said the "most likely" scenario is that the pace of growth of the Delta variant will "outmatch our supply of vaccines over the coming weeks".
Mr Reid said the modelling demonstrates that the cases of Delta here "will rise during July and probably peak into August".
"We know we won't have all of the adult population vaccinated by then, so in essence, the cases are rising before we have caught and vaccinated the significant element of the adult population," he said.
The comments came as the Department of Health reported 534 new cases of Covid-19, with 58 patients in hospital, of which 17 are in ICU.
The HSE's Chief Clinical Officer said the Delta strain now accounts for 70% of Ireland's cases, adding that it is "the dominant" strain and "we expect it to get higher".
Dr Colm Henry said the 14-day average of Covid-19 cases is 121 per 100,000 - up 20% on last week - and is highest in Donegal and Dublin.
The five-day moving average is 462, which is up 44% on last week. Over 55% of cases in the past week were in the 18-44 age group, he added.
Dr Henry said 2.4% were over 65 and 30% were in the 0-18 age group. "[The] rapid rise in cases is definitely not good news," he said.
Paul Reid says that the HSE is closely monitoring hospital numbers. He says that the HSE has not "as yet" seen a rise in the numbers of Covid-19 cases in hospital | https://t.co/XhZX2bb6gJ pic.twitter.com/CR2KekSkbs— RTÉ News (@rtenews) July 8, 2021
Mr Reid said the executive is monitoring numbers in hospital "very closely", but it has not seen a rise at this stage in the number of Covid-19 cases in hospital.
"It's important to remember that we have over 260 people in our ICU today, and almost 11,000 inpatients, so we do face into Delta from a high base, or hospitalisation perspective."
Mr Reid said that there are 301 ICU beds available to the HSE.
He said community testing is "as high" as it was on 11 January. The positivity level is 4.6%, versus the 50% positivity rate on 11 January, he added.
Mr Reid said the highest rate of positivity at a testing centre is in Donegal at 11%.
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Dr Colm Henry says that the Delta variant of Covid-19 now accounts for 70% of cases in Ireland. He says that it is "now the dominant" variant | https://t.co/XhZX2bb6gJ pic.twitter.com/ApfuFeMJAW— RTÉ News (@rtenews) July 8, 2021
EU Digital Covid Certificate not a prerequisite for travel
Meanwhile, Minister of State Ossian Smyth has said the EU Digital Covid Certificate will not be a prerequisite for travel, but it will make the process quicker.
Speaking on RTÉ's Morning Ireland, he said that if for any reason a person does not have the certificate, they can still travel on existing documentation.
Current Government advice is to avoid non-essential international travel, but it expects to reopen Ireland to international travel on 19 July.
People who are fully vaccinated will receive their EU Digital Covid Certificates by either email or post from next Monday
Mr Smyth said the certificate is a "whole of Government project" and said he does not foresee any difficulties with different departments coordinating on the project.
For those who are planning to travel on 19 July or soon after, but have not received their cert, Minister Smyth said they can still travel on their existing documentation.
"The vast majority of people will be okay," he said.
"I think there will certainly be exceptional cases, and the gov.ie website is there to help you, the call centre will be there to help you. I really just want to reassure people that you can travel on your existing documentation if you need to. Everybody has a way out."
'We are not out of the woods'
The World Health Organization's Special Envoy on Covid-19 said "we are not out of the woods yet".
Dr David Nabarro said that although he is fully vaccinated against Covid-19, he does not feel it is safe enough to return to international travel.
Speaking on RTÉ's Today with Claire Byrne, he said: "I'm super aware that this virus is really beastly, it is not a trivial virus at all and it's mutating and there are more variants and I am afraid just for now I am not travelling and if I do travel, I am going to be really careful.
"I will continue to mask. I will continue to distance. We are not out of the woods yet."
Dr Nabarro also urged caution against lifting restrictions too quickly and said medical advice has consistently been to keep some social distancing guidelines in place.
He said: "It's as though somebody has blown a whistle and we can all just stop all of the things that we've done and we can just go back and socialise like normal and it's okay, and I just wonder who it is who decided that somehow it's all okay.
"Nobody in public health is saying somehow it's all okay."