The 133 cases were among 231 positive tests nationwide reported on Saturday.
Taoiseach Micheal Martin and acting chief medical officer Dr Ronan Glynn both emphasised the need for people in Dublin to limit their social contacts.
In response to the increase in infections, the HSE opened two new pop-up testing facilities in the city on Saturday, at Croke Park and at Castleknock Health Centre.
There were no further deaths linked to the virus reported on Saturday, with Ireland’s death toll remaining at 1,777.
Commenting on the situation in Dublin, Dr Glynn stressed the importance of social distancing.
“While there is a significant number of cases in Dublin today, it is important to look at the day’s figures in the context of our seven and 14-day incidence rates,” he said.
“NPHET (National Public Health Emergency Team) pays close attention to trends and patterns in the data over time in order to analyse the progression of Covid-19 both across the country and in particular areas or settings.
“However, it is now really important that people in Dublin keep their social contacts as low as possible.”
He urged anyone with symptoms to self-isolate immediately and contact their GP.
“Given the increase in the number of cases in Dublin, the HSE has opened two pop-up Covid-19 swabbing centres in Dublin this weekend, at Croke Park and at Castleknock Health Centre,” Dr Glynn added.
“Please come forward for testing if you have any concerns. Remember that if you do need a test, it will be free.”
It is crucially important that we all heed the words of @ronan_glynn this evening. Please limit your social contacts and if you have any of the #COVID19 symptoms please phone your GP
— Micheál Martin (@MichealMartinTD) September 5, 2020
Mr Martin later tweeted: “It is crucially important that we all heed the words of @ronan_glynn this evening. Please limit your social contacts and if you have any of the #COVID19 symptoms please phone your GP.”
The 231 new cases take to 29,534 the number of confirmed Covid-19 cases since the outbreak began.
Across the border in Northern Ireland there were 118 new confirmed cases of coronavirus reported by the region’s Department of Health on Saturday.
While the department’s statistical dashboard provides updates on the number of positive test results over the weekend, it does not relay up-to-date information on coronavirus fatalities on Saturdays and Sundays.
The latest death toll reported by the department on Friday stood at 564.
