The Department of Health has reported 581 new cases of Covid-19.
Sixty coronavirus patients are in hospital, with 17 being treated in ICU, which is up one from yesterday.
It is the highest number in hospital in more than three weeks and compares to a figure of 44 people in hospital on this day last week.
Chief Medical Officer Dr Tony Holohan said: "We are continuing to see an increase in the incidence rate of Covid-19, and so, it is important that we do as much as possible to control the spread of the disease as the vaccination programme opens to all adults over the age of 18.
"The continuing high levels of adherence to the public health advice, high levels of vaccine uptake and community engagement with testing centres around the country are all reasons to be positive.
"If you display any symptoms of Covid-19, it is important that you isolate straight away and come forward for a PCR test."
Meanwhile, people aged 34 can register for a mRNA vaccine on the Health Service Executive vaccination portal from today.
Minister for Health Stephen Donnelly has confirmed that those aged between 30 and 33 will be able to register on the same portal from tomorrow to Sunday.
Those in the 18-34 cohort can also opt to receive the single-dose Janssen (Johnson & Johnson) vaccine with their local pharmacy.
The estimate for the number of unvaccinated people in the 18-34 age group is about 800,000.
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The Taoiseach said progress is being made in discussions on the reopening of indoor hospitality, and engagement with the sector will continue over the coming days.
Micheál Martin told a meeting of the Fianna Fáil parliamentary party this evening that the roll-out of the Covid certificate is on track for 19 July.
He said the Delta variant of the virus is a "slow burner" and the "central focus" of Government is to protect progress already made.
He said the Government owes it to young people to protect them, and it is doing so by accelerating the vaccine roll-out.
Minister for Health Stephen Donnelly said all over-60s will have their second dose of AstraZeneca by the end of next week.
He was responding after concerns were raised at the Fianna Fáil parliamentary party meeting, by Cormac Devlin and Malcolm Byrne, who said HSE Live is telling people it could be late July or August before they get their second dose.
They said this is different to the HSE's public statements.
Minister Donnelly also told the meeting that he expects people aged between 30 and 34 who have registered with the online portal to start receiving appointments from next week.
Health Service Executive CEO Paul Reid has said that more than 100,000 vaccines have been administered so far this week, with over half the adult population in Ireland fully vaccinated against Covid-19.
In a post this morning on Twitter, he said that by today over five million vaccines will have been administered.
Over 100,000 further vaccines administered already this week with 51.5% of the adult population now fully vaccinated and over 69% had a Dose 1. By today over 5M vaccines will have been administered in total. Every day counts. @HSELive— Paul Reid (@paulreiddublin) July 7, 2021
However, he later tweeted a correction to say that almost 4.5 million doses have been administered.
Correction, apologies, almost 4.5M vaccines in total by today Too early for all of those figures!— Paul Reid (@paulreiddublin) July 7, 2021
Immunologist Professor Luke O'Neill has said it is a travesty that people in the 60-69 age cohort, who received a first dose of the AstraZeneca vaccine are still not fully vaccinated.
Speaking on RTÉ's Today with Claire Byrne, he said this cohort should have received a mixed dose regime.
"It is a travesty that they aren't fully vaccinated. It is ridiculous in my view, because they are a vulnerable group. They should have been given the mRNA vaccine as a second shot," he said.
People who are fully vaccinated will receive their EU Digital Covid Certificates by either email or post from next Monday, under plans being finalised by the Government.
Minister for Transport Eamon Ryan said "he was confident" the system would "be in place and working well" by 19 July, when it is expected the country will reopen to international travel.
However, Prof O'Neill said people who are vulnerable should "think twice" about travelling abroad, even if they are fully vaccinated.
He said people must have "common sense" when deciding where to travel, as "it depends on where you are going" and the level of virus in a country or region.
Elsewhere, a further 570 positive cases of Covid-19 have been reported in Northern Ireland.
There were no deaths reported in the past 24 hours.
This morning, there were 43 Covid-positive patients in hospital, of whom four were in intensive care.
To date 2,089,386 vaccines have been administered in Northern Ireland.
Additional reporting Fergal O'Brien