Update 3.15pm by Daniel McConnell: Fifty new hospital beds will be opened nationwide today, while 760 wait on trolleys.
Visiting restrictions have been put in place at six separate hospitals around the country in an effort to prevent the spread of the flu.
Hospitals in Waterford, Limerick, South Tipperary and Cork have all put a visitor plan in place.
Elective surgeries have also been cancelled in some locations and the public are being urged to visit their GP if they have flu-like symptoms.
Health Minister Simon Harris is promising to open 199 new beds by the end of the month.
Minister Harris said: "There have been no resources that have been sought from the Government by the HSE that haven't been provided in terms of wanting to assist and when I met the HSE this morning, I reiterated that we are willing as a government to do what it takes to provide our hospitals with the support during this difficult period.
"But there is a reality in terms of the limitations with capacity and the fact that it is taking time to build that capacity back up."
He added that this week is set to be “very challenging” in terms of containing the numbers of people on trolleys in the country's hospitals.
Speaking to the media alongside Taoiseach Leo Varadkar, Mr Harris said they were told by the HSE this morning that the demand for home care packages is near record lows, meaning there is not a problem with bed blockers.
Mr Harris said the difficulty is that too many people are simply too sick to be discharged from acute hospitals.
Both Mr Varadkar and Mr Harris called on the public to heed the HSE's advice to stay away from hospitals where possible.
“It's important to bear in mind that the advice around not visiting hospitals should be heeded. But that's not primarily about overcrowding that's about infection control,” the Taoiseach said.
“Because when you have a lot of patients that are hospitals who have influenza. We don't want more people getting infected and therefore spreading the virus virus even more so within the community so that's why the advice is there to people, not to visit hospitals unnecessarily,” the Taoiseach said.
“So 50 more beds opening today, and more to come at the end of the week more to come again next week to talk to 199 additional beds by the end of this month,” Mr Harris said.
“So in this week is going to be very challenging. And we have to prioritize Patient Safety first. The doctors will discharge patients as appropriate. A number of people to be discharged today I think I'll say discharge figures, with over 600 today will be discharged,” he said.
Update 1.45pm by Vivienne Clarke: The HSE’s national director of acute hospitals has admitted that there is a shortage of hospital beds and gaps in community care. While he disputed figures from the INMO, he acknowledged “this is not a good day” for the health service.
Liam Woods told RTÉ radio’s News at One that there are “real pressures” on the system, but that capacity will improve with 190 beds due to open in the first quarter of this year.
He said that 40 beds will open in a new unit in Clonmel in the next four weeks, with further beds due to open in Drogheda and Waterford.
While the flu season peaked in weeks 51 and 52, the pressure will be felt in the following two to three weeks. Mr Woods also said that there is a risk of a double incident of the flu, particularly with the return to school this week and the increased risk of infection.
He advised parents that if their children are ill to keep them at home.
A number of measures were being taken he said, such as the curtailment of elective surgery, use of the private sector and community initiatives such as sending doctors out into the community in cars rather than having patients come into surgery or hospitals.
It was normal for elective surgery to be curtailed at this time of year, he said, it was a move that the HSE was reluctant to take, but it was an ongoing daily intervention.
Mr Woods also pointed out the pressure that the GP out of hours service is operating under with an increase of 20 per cent in patients in some sites.
His advice to the public is self care, then their GP, but that “hospitals “will always be there to treat patients who need hospitalisation.”
Update 10.37am By Denise O'Donoghue: 760 admitted patients are going without beds in Ireland’s hospitals this morning – the worst-ever figure since records began.
According to the INMO, the number of patients on trolleys this morning would fill the largest hospital in the state, St. James, which has 707 beds, or take more than twice the equivalent of Letterkenny University Hospital's 333 beds.
The previous worst-ever day was March 12, 2018, during the “Beast from the East”, when 714 patients went without beds.
University Hospital Limerick has also broken the daily record for an individual hospital, with 92 patients on trolleys. The previous highest figure was 82, also in UHL.
Visitors have been banned from UHL due to the high number of people it is treating for flu. The only exceptions to the visiting ban are people visiting patients who are at end-of-life, are critically ill or who have dementia. Parents visiting paediatric patients are also exempt.
CUH saw a record daily high of 73 waiting on trolleys last week, but today that figure is 56.
The INMO is calling for a major incident protocol to be adopted across the country, as was done in March 2018. This would likely see all non-emergency admissions stopped, electives cancelled, and extra bed capacity sourced from the private and public sectors.
The union is also calling for an infection control plan, as overcrowding increases infection risks.
"Ireland’s beleaguered health service continues to break records in the worst possible way. Our members are working in impossible conditions to provide the best care they can," said INMO General Secretary, Phil Ní Sheaghdha.
"The government need to immediately initiate a major incident protocol. We need to cancel elective surgeries, stop non-emergency admissions, and source extra capacity wherever we can.
"We also need to immediately scrap the HSE’s counterproductive recruitment pause, which is leaving these services understaffed and thus overcrowded.
"Behind these numbers are hundreds of individual vulnerable patients – it is a simply shameful situation. This is entirely preventable if proper planning was in place."
Last year, over 118,000 patients found themselves waiting for a bed in hospital.