A further 1,558 cases of Covid-19 were reported in the State on Monday.
There are 262 people in hospital with the disease, 51 of whom are in ICU.
Speaking as the latest figures were released, chief medical officer Dr Tony Holohan said: “Though we have growing levels of vaccination across the population, there is now a very high level of disease circulating in the community. The Delta variant has enabled Covid-19 to regain a foothold in Ireland, which puts us all at risk as social contacts and mobility increase.We are closely monitoring the spread of the virus with some concern.
Dr Holohan said vaccinations would help “turn the tide, but we are not there yet”.
“We need to give vaccines the time and space to build up levels of protection across all demographics so that we can continue to progress the reopening of all sectors of society and our economy,” he said.
Mr Holohan called on people to get vaccinated as soon as one is offered to them and he reminded people to ensure they get their second dose.
He said: “You will be fully protected one or two weeks after your second dose, depending on which vaccine you have received.”
Dr Holohan asked people to continue following public health advice, particularly in the run up to schools reopening in September.
“If you have any symptoms that indicate that you may have Covid-19 like cough, fever, headache, sore throat and blocked or runny nose isolate and get a test immediately,” he said.
“Make plans to socialise safely and risk assess as you go, meet up with others outdoors if possible, try to meet up in small groups and avoid crowds. If you do not feel safe, then leave.”
Ireland has the second highest rate of full vaccination in the European Union, according to figures produced by the European Centre for Disease Prevention and Control (ECDC).
With 80.7 per cent of the adult population fully vaccinated, only Malta with a figure 87.80 per cent has had a more comprehensive vaccination programme to date. Ireland is one of only three EU countries where more than 80 per cent of the population is fully vaccinated, the other being Belgium with a share of 80.6 per cent.
The EU average of fully vaccinated adults is 63.2 per cent while 73.6 per cent of adults have had at least one dose.
The figure in Ireland for adults with at least one dose is almost 90 per cent (89.9 per cent).
Just 18.6 per cent of adults in Bulgaria are fully vaccinated, the lowest rate in the EU.
Commenting on the figures, Minister for Health Stephen Donnelly said the vaccine rollout was a “reflection of the huge work being done by our vaccine teams, GPs, pharmacists and so many others across the country”.
Earlier, the HSE’s national lead for testing and tracing, Niamh O’Beirne, said they are following up on positive cases of Covid-19 on up to 30 flights per day.
While the level of transmission on flights was quite low, she told RTÉ radio's Today show, when a positive case was linked to travel, they had to track and trace the other passengers in the two rows in front, behind and to the side of the infected person. This could be up to 500 people (over the 30 flights).
It comes as there were a further 1,758 new cases of Covid-19 reported in the State on Sunday, while 248 people were in hospital with the virus, and 48 in intensive care.
There were 110 to 120 outbreaks per week, she explained, with the majority from social gatherings and workplaces. Travel constituted about 7.5 per cent of cases recently, with a range of five percent to 10 per cent.
In the majority of cases connected to flights it was “most likely” that the people had already been infected before they got on the flight, she said.
With regard to workplace cases these were related to a return to the workplace, transport, people going to work who were symptomatic and people moving around the office during breaks.
Ms O’Beirne urged people to continue to wear their mask once they get up from their desk and to observe social distancing measures.
Social gatherings such as weddings were also contributing to increased transmissions. In one case there had been 30 positive cases out of 50 people who attended the wedding.
Having 2,000 cases per day made tracking and tracing a real challenge, she added. Identifying close contacts, those who were vaccinated and unvaccinated was necessary so they could determine who should get tested. There was also the issue that 20 per cent of people did not know all their contacts.
Meanwhile, consideration is also being given to narrower terms for Covid-19 testing. However, strong public health, testing and contact-tracing capacities would be retained for rapid management of outbreaks.
However, there is “profound concern” among public health officials that deterioration in the disease in the coming weeks could make progress harder to achieve, especially if basic hygiene measures are abandoned while vaccination is still under way.
There is concern the current Delta wave could harm the chances of progressing. It is expected there could be in the region of 400 people in hospital with Covid at the end of the month, at which point Health Service Executive chief executive Paul Reid said the impact on the healthcare system becomes harder to manage.
“It’s looking... that we could get to 400 soon, because of the lag effect of these consistent high case numbers,” Mr Reid told The Irish Times, but he said there was no current need to scale back routine health services on a national level.
Meanwhile, three more people have died with Covid-19 in Northern Ireland, the North’s Department of Health reported on Monday.
A further 1,306 people tested positive for the virus.
In the last seven days almost 1,000 cases of the virus have been confirmed in the North.
A total of 344 patients are receiving hospital treatment for Covid-19 in the North’s hospitals, with 11 in intensive care.