he chief medical officer, who chairs Nphet, and the deputy CMO received the “sinister” calls on Friday.
In the case of Dr Glynn, the call was made to his landline. A member of his family answered and was subjected to the “abuse”, according to sources.
Gardaí were contacted in both instances and are now investigating.
Security sources said garda technical experts, who are experienced in tracking calls, are now attempting to establish where the calls came from.
“The calls are best described as sinister and menacing rather than death threats. Let’s not give these people behind it too much credit. It isn’t too difficult to establish where people live,” a source said.
“An incident like this is very difficult for any person involved. These senior people in Nphet have been in the public limelight and it’s very unfortunate and unfair they have to deal with this. It will be fully investigated.”
Last night detectives examining the menacing phone calls to Dr Holohan and Dr Glynn were trying to establish if there was a link between the threatening calls and a third made to RTÉ’s health correspondent Fergal Bowers.
“All of these matters are under investigation,” a source said.
“There seems to be no apparent link in terms of the nature of the calls, the voices and what exactly was said but it is still early days in this investigation.”
A garda spokesman said: “A number of reports of menacing phone calls have been reported to An Garda Síochána and these matters will be fully investigated. It is not appropriate to comment further at this time.”
Mr Bowers shared a recording of a voice message on social media yesterday. He said he received the call just after 3am.
He said he was “alerting the relevant authorities”.
Government Ministers have condemned the abusive phone calls aimed at the public health officials.
Health Minister Stephen Donnelly called the abuse “absolutely appalling”, adding that the public health doctors have worked “relentlessly” during the pandemic and deserve respect.
Mr Donnelly said on Twitter, “It is absolutely appalling that public health doctors advising Government would be targeted with abuse for doing their jobs in the middle of a pandemic.
"They have worked relentlessly throughout Covid and have difficult jobs to do. They deserve our respect and support.”
Meanwhile, Minister Simon Harris said he is “sickened” to hear of the abusive calls directed at Dr Holohan and Dr Glynn and their families.
Mr Harris said on Twitter, “Our public health officials have been working around the clock for well over a year now to keep us safe & provide us with the best possible expert advice.
“Sickened to hear of abusive calls being directed at them & their families.”
It comes as the Government is unlikely to allow the resumption of children’s indoor summer camps as well as christenings, communions, and confirmations over the summer months.
The Sunday Independent understands that senior public health officials are concerned about the potentially disastrous consequences of the Delta variant spreading among unvaccinated children.
They are also worried at the potential for this to lead to the infection of a small proportion of the vaccinated population. These are so-called breakthrough infections.
The Government last week asked Nphet to consider the resumption of religious ceremonies including christenings, communions and confirmations, and a safe way to allow indoor summer camps over the summer.
While Nphet is expected to advise the Government in the next two weeks, senior Government sources acknowledged this weekend that allowing such activities may be off the table for the foreseeable future.
“Nphet thinks children are now a big part of it as they transmit the virus. But they are kids — the risk to them of getting sick and hospitalised is very low,” one senior source said.
A second senior source said: “Indoor activities for the unvaccinated are to be avoided.”
Despite the surge in the Delta variant, the Government remains confident that plans to resume indoor dining and drinking for people who are vaccinated can go ahead from July 26, a week tomorrow.
One insider described “a little bit of anxiety” within the political system over the plans.
But the Government hopes that the distinction between unvaccinated and vaccinated will drive uptake of vaccines among those who have yet to avail of one.
Concern at the impact of the spread of the Delta Covid variant has heightened in recent days as daily case numbers rose sharply in the second half of last week.
Ireland is currently reporting its highest five-day average of Covid-19 cases since the middle of February.
Deputy chief medical officer Dr Glynn said the incidence has risen to more than 180 cases per 100,000 people, and the country is reporting a five-day average of more than 800 cases a day.
Yesterday the Department of Health confirmed it had been notified of 1,377 new cases of the virus.
Experts fear Ireland could reach 2,000 cases per day by the end of July.
Anthony Staines, professor of health systems at Dublin City University, said the recent trajectory of cases had been worse than anticipated.
“Unfortunately, I do think we could end up in another lockdown. The Government should be embarrassed if we do,” Professor Staines said.
“The purpose of lockdowns is to use that time to properly implement track and trace systems, which they failed to do.”
Government officials and representatives from the hospitality industry are to finalise plans for guidelines for the sector early this week.
One issue that has emerged in recent days is whether businesses will have to hire extra staff to check vaccine certificates at points of entry.
This could be particularly problematic in shopping-centre food courts and large petrol stations. The industry argues that people who are sitting in to eat should have their vaccination status checked at the tills when purchasing food and drink, rather than by a separate staff member.
Meanwhile, there is uncertainty this weekend over the Government’s deal to buy a million Covid-19 vaccines from Romania.
The deal was announced in principle by Taoiseach Micheál Martin on July 2 following talks with Romanian President Klaus Iohannis.
However, a fortnight on there is little information on when the doses of Pfzier and Moderna will arrive in Ireland.
A senior source said their understanding was the deal relates to vaccine doses due to be allocated to Romania — and not ones the eastern European country already holds.
The European Commission has also become involved and is pushing to ensure a deal is done centrally rather than as an individual matter between Ireland and Romania.
In response to queries, a Department of Health spokesperson said: “Ireland is engaged in discussions with a number of Member States regarding the availability of surplus Covid-19 vaccines.
"It is inappropriate, given the confidential and ongoing nature of these discussions, to comment further at this time.”