The reproductive rate of the coronavirus is closer to one than it has been in recent weeks, health officials have warned.
It comes as there have been five further deaths in relation to COVID-19 - there are also 15 new cases of the virus here.
It brings the overall death toll to 1,738 and 25,489 cases.
The National Public Health Emergency Team (NPHET) met earlier to review Ireland’s ongoing response.
Professor Philip Nolan is chair of the NPHET Irish Epidemiological Modelling Advisory Group.
He said: "The reproductive number is now estimated to be closer to one than it has been in recent weeks.
"The 'R' number is easily influenced by small changes to the transmission of the virus.
“We have noticed an increase in the number of cases towards the end of last week.
"It is a trend that NPHET will continue to monitor closely."
There has also been an increase in the number of cases associated with foreign travel.
This slide shows how #COVID19 is being transmitted.
The majority (>60%) of cases in recent weeks are close contacts of confirmed cases, community or possible community transmission.
Note the re-emergence of travel-related #COVID19 cases. pic.twitter.com/slaY4puZFM— Department of Health (@roinnslainte) July 2, 2020
Dr Tony Holohan, Chief Medical Officer, said: "What has been a collective and effective national effort to suppress COVID-19 in Ireland, now also becomes an individual mission.
"Every person must risk assess their own environments, make appropriate decisions about where they will go and who they will meet, and how they can ensure their safety and the safety of those around them.
"Continue to follow public health advice, understand the risks of your actions and environments and stay safe."
Dr Ronan Glynn, Deputy Chief Medical Officer, said: "60% of all COVID-19 cases have been reported in the past month.
"The transmission of the virus is accelerating globally.
"In order to limit the potential for a resurgence of the disease in Ireland, we all must continue to follow public health advice and take responsibility for our individual actions."
And Dr Vida Hamilton, national clinical advisor at the HSE said: "Due to the good practices of the public our ICU’s were not overwhelmed.
"Although they were busy, every patient got the care they deserved.
"Some of us may have witnessed the reality of the frontlines in our hospitals on recent television documentaries.
"We should not lose sight of what is at risk and how fragile our systems are in the face of this pandemic. Please continue to follow public health advice."
