There are 102 new confirmed cases of the coronavirus in the Republic of Ireland.
There are now 785 cases of COVID-19 in Ireland.
The HSE said it is now working to identify any contacts the patients may have had to provide them with information and advice to prevent further spread.
The virus has claimed three lives in Ireland so far.
Speaking on Saturday evening, Dr Tony Holohan said: “The Department is aware that pubs in some areas of the country are continuing to open, in contravention of existing public health advice.
"If any such premises become known to us, the Minister will be advised to use his regulatory powers to enforce the temporary closure of premises in order to prevent the spread of Covid-19.
“We are also asking An Garda Siochana to assist in encouraging the public to abide by the public health advice on social distancing by encouraging any groups congregating in public to disperse.”
As of midnight on Thursday, 147 of the notified cases, about one in four, are associated with healthcare workers.
55% of patients are male, 44% women and 1% is unknown. The median age of those with the virus is 44.
More than 10,000 people in the country have been tested.
Dublin has the highest number of cases with 55%, followed by Cork 15%, according to data from the HPSC which is relevant up to midnight on Thursday.
Three in 10 people who have tested positive have been hospitalised, with 2% of patients being submitted to ICU.
Dr Ronan Glynn, Deputy Chief Medical Officer, Department of Health, added: “We must continue in our efforts to limit the spread of Covid-19 together, as a society, to protect our healthcare workers and our most vulnerable.”
A new testing centre being built in Tullamore, Co Offaly is believed to be one of several facilities to be constructed over the next few days.
Earlier on Saturday, the North announced a further 22 cases bringing its total confirmed cases to 108. One person in Northern Ireland has died as a result of Covid-19.
A spokesman for the NI Department of Health said: “As of 2pm on Saturday 21 March, testing has resulted in 22 new positive cases, bringing the total number of confirmed cases in Northern Ireland to 108.
“To date 1 person who tested positive has sadly died.
“The total number of tests completed in Northern Ireland is 2,186.
“People with mild symptoms - new persistent cough and/or fever - should stay at home and self-isolate.
"They will not require testing and will not therefore be included in testing totals.”
