Taoiseach Micheal Martin has said that any spike in coronavirus cases is of concern.
He said the Government will “watch and monitor very carefully” what happens with the number of Covid-19 cases in the coming days.
It came as health chiefs in the Republic said that 85 new cases reported on Thursday were a worrying escalation.
A factory in Kildare and at least two direct provision centres in the Midlands, where some of the workers live, have created a cluster of infection.
Construction sites are also linked to the sudden increase, health officials said.
On Friday, another 38 cases were confirmed by the National Public Health Emergency Team, bringing the total to 26,065.
However no further deaths had been notified as of midnight on Thursday, leaving the national total at 1,763.
Speaking at Dublin Castle before the start of the North South Ministerial Council (NSMC), Mr Martin said: “Obviously any spike at all we are concerned about.
“We have to watch and monitor very carefully what happens now over the next number of days in terms of whether that is a pattern or whether it’s relating to specific clusters that have emerged in recent days.
“What is heartening is the response of the testing and contact tracing apparatus now within the Republic.”
If you have these symptoms 👇 call your doctor immediately and ask about a coronavirus test:— HSE Ireland (@HSELive) July 31, 2020
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He said he spoke to Dr Ronan Glynn on Thursday evening and that the acting chief medical officer is “quite intensive” in getting on top of testing and contact tracing.
A total of 18 of Thursday’s tally were associated with the factory.
Meanwhile, Mr Martin said the Cabinet will meet on Tuesday to decide whether the country can move to phase four of the road map and allow pubs that do not serve food to reopen.
He said it will depend on whether the number of cases decreases.
“We will see what the National Public Health Emergency Team (NPHET) have to say,” he said. “We won’t draw too much inferences from the 85 new cases yesterday … we have to see if a pattern has emerged or if it was a cluster.”
Dr Glynn later confirmed mass testing had now taken place in relation to a number of known outbreaks.
“We may be beginning to see more cases which we cannot link to outbreaks or close contacts,” he said.
“The National Public Health Emergency Team will continue to monitor this situation closely over the coming days.
“The importance of isolating as soon as you have any flu-like symptoms cannot be overstated. Without this individual action we simply will not break the chains of transmission and we will put many people at risk of infection.
“It is important that people know that there is no charge for GP or testing services relating to Covid-19. Please do not hesitate to contact your GP if you have any concerns.
“This weekend, the six key things people need to do are limit the size of your network & time you spend with them, keep your distance, meet up outside if possible, wash your hands, wear a face covering and download the Covid tracker app.”