People are being urged to avoid crowds and continue to follow "basic public health measures", as the Department of Health has reported 589 new cases of Covid-19.
The number of people in hospital with the disease is 62, of whom 17 are in ICU, one more than yesterday.
Dr Ronan Glynn, Deputy Chief Medical Officer, said: "Scientific evidence shows that Delta is a much more transmissible variant of Covid-19, now accounting for 80% of the cases reported in Ireland.
"This is a challenge that is facing all of Europe, but we know that the basic public health measures still work against this variant.
"Please continue to avoid crowds, wear a mask, manage your contacts, keep your distance, meet outdoors where possible and if indoors, ensure that the room is well ventilated."
Dr Glynn added: "We are asking anyone diagnosed with Covid-19 to work with our contact tracers to identify all of your close contacts so they, their families and colleagues can be protected.
"If you know you are a close contact of someone with Covid-19, or if you have any symptoms, stay at home and organise a free test as soon as possible."
There were 511 new infections and no further deaths notified in Northern Ireland today.
More than 57% of adults in Ireland are now fully vaccinated while 72% have received at least one vaccine dose, according to Brian MacCraith, Chair of the High Level Task Force on Covid-19 vaccination.
HSE chief executive Paul Reid has said there are "warning signals of increased testing, cases and positivity" as the Delta variant spreads in Ireland.
Despite the increasing numbers of adults being vaccinated, Mr Reid warned of a "very risky few weeks ahead".
"Some of our centres across the country have seen 14% positivity rates," he said. "Not quite at the 35% to 50% positivity rates that were seen in January, but still a rising concern for us."
Mr Reid said it provides "a really strong signal to the public to continue to keep our guard."
"Vaccines will ultimately win, but the next few weeks are important that we stay ahead and protect ourselves through public health measures," he added.
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Earlier, Minister for Health Stephen Donnelly told the Dáil that the hospital system has been "close to full capacity in recent weeks", and that this has caused "distress" to staff and patients.
As of 4 July, admissions were up 12% on the same period in 2019, he said.
During Priority Questions to the Minister for Health, Sinn Féin's David Cullinane said that over-crowding in acute hospitals is "very close to being back at pre-pandemic levels".
Minister Donnelly said that 834 additional acute beds had been delivered, with 229 more expected this year.
73 sub-acute beds have been added, with 40 more planned for this year, he said.
The baseline ICU capacity is now 297 beds, the minister said. The aim is to increase that to 331 by the end of this year.
Elsewhere, a million EU Digital Covid Certificates are being issued by email to people who were fully vaccinated at a Health Service Executive vaccination centre.
Meanwhile Sinn Féin, Labour, and the Social Democrats have all raised concerns that the policy of excluding unvaccinated people from indoor hospitality is discriminatory.
Earlier, Taoiseach Micheál Martin said that compliance with the new rules around indoor dining and drinking is something the public will have to "buy into".
It comes as the European Medicines Agency (EMA) said it was analysing data on rare cases of a nerve disorder reported among recipients of Janssen (Johnson & Johnson) Covid-19 vaccine, after the United States added a warning label to the shot.
The "EMA's safety committee (PRAC) is analysing data provided by (J&J) ... on cases of Guillain-Barre syndrome (GBS) reported following vaccination," the European medicine regulator said in a statement to Reuters.
Also today, a new survey of almost 2,000 parents found that 60% identified anxiety as a long-term impact of the Covid-19 pandemic on their children's mental health.
The overuse of social media during the pandemic and stress were also identified as areas of concern, with 26% and 27% of parents citing these respectively.
Yesterday evening, Chief Medical Officer Dr Tony Holohan used the 500th day since Ireland's first confirmed case of Covid-19 to warn of the threat posed by the Delta variant to those who have yet to be fully vaccinated.
The official number of people who have died after contracting the virus is 5,006, and some 278,000 cases of infection have been recorded in the country.
"As we approach our 5 millionth dose of the Covid-19 vaccine, we have great hope for our future," he said in a statement.
"We have come so far, and I know it is hard to continue to adhere to the public health measures, but our continued individual effort is needed to minimise the risk of the Delta variant, a highly transmissible strain that poses a significant threat to the unvaccinated or partially vaccinated."
