A total of 600 new cases of Covid-19 were notified in the State on Monday evening with 64 patients in hospital and 16 in ICU.
Chief medical officer Dr Tony Holohan said there was a "worrying increase" in incidence of the virus among people in the 16 to 29 age group.
He urged unvaccinated and partially vaccinated people to “maintain a high degree of caution in your activities this summer”.
Dr Holohan added: “We have come a long way together on this difficult journey and sacrificed much in our collective effort to limit the transmission of this disease.
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“As we approach our five millionth dose of the Covid-19 vaccine, we have great hope for our future. Our vaccination programme is working, the levels of protection in the community against the virus are increasing daily and those who are fully vaccinated should feel safe to increase their social contacts and to take advantage of new freedoms, while continuing to make positive public health choices in their daily routine.
“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.”
His deputy Dr Ronan Glynn said the number of people in hospital as a result of Covid-19 remained "low" despite a 60 per cent increase in cases.
In the last three weeks since the Delta variant became dominant, the average number of new cases of the virus per day had risen from 300 to 500.
The number in hospital with Covid-19 reached a low for the year on June 25th of 38 and had since risen to 64 as of Monday evening.
The number in ICUs has remained steady despite 5,500 new cases of Covid-19 this month so far. The numbers in ICU have gone from 14 on July 1st to 16 on Monday.
At the peak of the pandemic in January there were more than 2,000 people in hospital and 221 in ICUs.
In a video posted on his Twitter account, Dr Glynn said the increase in hospital numbers have been “small but concerning” over the last week though they remain low.
All other indicators for the disease are on the increase, he said, with the percentage of people testing positive for Covid-19 increasing even while the number of people being tested was also increasing.
Dr Glynn said the number of cases which were a result of the Delta variant increased from 4 per cent in early June to more than 70 per cent and it continued to rise.
Hotspots for the Delta variant can be found in Donegal, Limerick and Dublin, he added, with incidences also increasing in Sligo, Limerick, Roscommon and Meath.
He stressed that the Delta variant was a worry because it is twice as transmissible as the first iteration of the virus last year. It can also affect people who have had only one dose of vaccine.
It was imperative, he added, that people get fully vaccinated as quickly as possible. People are fully vaccinated one week after the second dose of Pfizer, two weeks after the second dose of AstraZeneca or Moderna and two weeks after the single shot of Janssen.
He said people who are not fully vaccinated should minimise the contacts they have with other people and avoid crowded indoor settings.
Minister for Health Stephen Donnelly said five million vaccines will be administered by end of this week and Ireland has now surpassed the United States in terms of the uptake of the vaccine.
He said there is “very strong demand” from young people for the Janssen vaccine which is being administered in pharmacies to those aged between 18 and 34.
The plan is to administer all second doses of the Astra Zeneca vaccine this week.
On Monday the North's health department reported a further 528 positive cases of coronavirus in Northern Ireland. There were no further Covid-19 linked deaths reported in the past 24 hours.
So far 2,127,703 Covid vaccines have been administered in Northern Ireland.
