More than 100 St Patrick's Day parades and festivals are on the brink of cancellation as organisers face "significant pressure" to put public health first.
Organisers of dozens of events will meet over the next 72 hours to decide on the next steps, amid the ongoing coronavirus threat.
The Government decision to allow the major city parades to proceed has been criticised by both health officials and campaigners.
Last night it was confirmed that Ireland has two more cases of Covid-19, and significantly both were transmitted within the community.
The man in Cork and woman in the east of the country bring the total confirmed cases in the Republic to 21.
Previously there was only one case in Ireland that was not directly related to the outbreak of the virus in Italy.
Meanwhile, a former Dublin lord mayor and current chairperson of the capital's Central Area Committee are demanding the country's largest St Patrick's Day parade be called off immediately.
Independent councillors Christy Burke and Anthony Flynn are to table a motion at an emergency meeting of Dublin City Council for the parade - which attracts up to 500,000 people - to be cancelled indefinitely.
Speaking last night, Mr Burke said: "My phone is ringing non-stop with concerned people over the spread of the coronavirus - especially over the past 48 hours.
"Councillor Flynn and I believe we will have the full backing of our motion by all councillors on Tuesday. Taoiseach Leo Varadkar needs to finally listen to people on this and the feelings out there.
"The public don't want the parade to go ahead as people are going to be 20 deep and in close quarters trying to view it. It also makes its way from Parnell Square in the north of the city down to the south side.
"I've had people coming to be telling me they are leaving the city to get away from crowds of people for a few days.
"Our European counterparts are taking the coronavirus crisis very seriously and we as a nation need to take a more serious note out of their books."
However, amid mounting concern, Taoiseach Leo Varadkar's spokesman said a new administration "would not make it any easier" to deal with the outbreak.
A Cabinet sub-committee meets today to consider further measures.
Meanwhile, both new cases of the virus involved community transmission - underlining fears that the illness is spreading in Ireland.
The male in the south of the country is at the Bon Secours Hospital, Cork, and a risk assessment is under way.
"The patient is being cared for in a single room and contact precautions have been in place since the patient's arrival," a statement said.
It is understood the woman infected has an underlying medical condition.
The HSE said it "cannot dispute" that up to 1.9 million people in Ireland may be infected by the coronavirus.
However, speaking on RTE Radio, HSE chief executive Paul Reid said it was working to contain the virus and putting together "significant plans".
"Those plans are important and the most appropriate plans for this [containment] phase," he said.
He declined to dispute figures reported in the Sunday Business Post that up to 40pc of the population, or 1.9 million people, may contract the coronavirus.
"There's ranges you're seeing from 30pc to 50pc and indeed some less and very significant differences in terms of impact. We're working through that right now," he added.
When asked if the parade should be cancelled, Mr Reid said people would assemble regardless, adding: "We still will have concentrated numbers of people in different settings."
Pensioners and those with underlying health conditions are being advised not to attend gatherings like the festival.