The threat of Covid is 'still very real' according to HSE chief executive Paul Reid, who urged the public to "take good care".
On Sunday, the number of people in hospital with the virus reached its highest level since the end of March.
The Department of Health reported 1,688 new cases, with 314 patients in hospital, an increase of 55 from Saturday. The number of people in ICU is up five to 59.
In a tweet, Mr Reid said: “Vaccinations continue this weekend. Almost 6.6M now administered. 91% of adults partially vaccinated & 85% fully. 135,000 12-15s registered & 77,000 now administered.
“But the threat is still very real as 314 Covid-19 patients now hospitalised & 54 in ICU. Take good care.”
Minister for Foreign Affairs Simon Coveney said the Government will release a roadmap for the further reopening of society before the end of August.
He told RTÉ: “For a number of days now the number of people who tested positive is well over 2,000, and we see in Northern Ireland in the last few days the highest number of positive tests since this pandemic began, and we have seen now the numbers in hospital over 300 and the numbers in ICU over 50.
“The Delta variant is dangerous, it’s spreading and it’s present.”
It came after the Taoiseach warned that the Delta variant has not yet reached its peak in the country.
Micheál Martin said: “We are concerned about the Delta variant and the increase in numbers. At a meeting last week, the CMO (chief medical officer) articulated that concern along with the Nphet representatives and the CEO of the HSE in terms of the impact on hospitalisations and ICUs.
“So we did anticipate this increase, we anticipate an increase over the next number of weeks. We have not reached the peak of the Delta wave yet, and of course any time the disease is increasing at this rate is a time for concern.”
In anticipation of a surge in cases among teenagers when schools return over the coming weeks, the HSE is putting plans in place for Covid testing.
Currently, up to 15,000 tests are being carried out each day at HSE testing sites, and a further 10,000 being done privately and in hospitals.