The number of cases of Covid rose by 92 yesterday - with 24 of those occurring in the Dublin region.
Dr Ronan Glynn, acting chief medical officer, said: "We expected that this week the daily figures we report would rise and fall."
He said that the National Public Health Emergency Team (Nphet) is closely monitoring all trends, patterns and changes in the data, including not just case numbers, but locations, age groups and sources of transmission.
He asked people in Kildare, Laois, and Offaly to "hold firm" and urged them to "stay with us in the measures introduced last weekend."
Dr Glynn said the latest figures show that Covid-19 cases are increasing in other counties and that a "united" approach is needed in order to lower the risk of transmission.
"This is still about a united, whole-of-country approach. The only way we can effectively suppress Covid-19 across Ireland in the long term is if we act together to protect each other.
"Living with Covid-19 has undoubtedly been difficult and this pandemic has adversely impacted on people in many different ways.
"We know that what the public health advice asks you to do can be difficult, but we are asking you to stay the course with it."
No deaths were reported in the cases yesterday.
There are now a total of 26,929 confirmed cases of Covid-19 in Ireland and 1,774 coronavirus-related deaths.
Of the new cases notified, 24 are in Dublin, 24 in Kildare, eight in Limerick, six in Carlow, six in Kilkenny, five in Meath, five in Clare, and remaining 14 cases are in Cork, Donegal, Kerry, Laois, Louth, Monaghan, Offaly, Waterford and Wicklow.
Meanwhile, the Dáil coronavirus committee heard yesterday that workforce representation does not exist in meat plants, and when a worker contracts Covid-19 the Health and Safety Authority (HSA) is not notified.
"All the indicators to me are that the HSA don't want to be notified," claimed Irish Congress of Trade Unions (Ictu) leader Patricia King.
"They don't want this task. I am blue in the face writing out this. If they don't go to the places and carry out inspections, we will be in all sorts of a mess."
Greg Ennis of Siptu declared: "I believe we need Covid compliance inspectors. If we have to beef up the HSA, then beef it up - no pun intended."
The trade unions warn that Covid could prevail "for possibly years to come", but meat would always remain an essential foodstuff for the population.
Therefore there was "little choice but to shine a light like never before on this industry and address it once and for all," Mr Ennis said.
The meat industry had become the "perfect storm" for the transmission and predicted resurgence of Covid-19 in Ireland.
Nora Loba, of the Independent Workers Union, said the pace of output in plants had never slowed down, despite outbreaks. "When some workers got ill, others had to do more work," she said.
Worker representatives, where they existed, had never been consulted about any protocols. The key problem was that workers were in substandard employment, on minimum wage with no sick pay, and had overcrowded living conditions.
The Covid crisis in meat plants was the inevitable consequence of the "long-term disregard of staff".
On minimum wage with no overtime, they had to work long hours - with no time to go to the doctor or to learn English to communicate any problems.
James Lawless of Kildare North, a Fianna Fáil TD and former branch secretary of the trade union Unite, said the three locked-down counties had been psychologically damaged.
"Three counties are paying the price for three or four plants," he said.
Siptu said the early experiences of meat processing plants in the US, Canada and across the European Union should have given notice of what was on the way for Ireland.
"Siptu publicly called for mandatory temperature testing to be put in place for workers within the meat industry," Mr Ennis said, and the union had complained in April to the HSA, while requesting inspections at a particular facility.
In May the union wrote to Meat Industry Ireland seeking a meeting, but was refused. It repeated its calls for speedy blanket testing of workers.
"It is now beyond doubt that the meat processing industry contains unrivalled vectors for the transmission of Covid-19, which had previously caused 1,115 meat plant workers to be infected in 20 clusters, as of early July," Mr Ennis said.
The risk factors include close-proximity working, bottlenecks in canteens and toilets, and noise pollution causing workers to shout to communicate - creating droplets, with these circulated through the industrial air-cooling systems.
Nine in 10 do not get sick pay, forcing vulnerable workers to go to work - even if they are feeling unwell with possible Covid symptoms - he added.