Minister for Health Leo Varadkar has said that he believes the overcrowding situation at Beaumont Hospital should ease in a few days.
The Irish Nurses and Midwives' Organisation has said 386 people are waiting in hospital Emergency Departments, or on wards for admission to a hospital bed.
Beaumont Hospital in Dublin has again asked people to avoid visits to its Emergency Department unless it is absolutely necessary.
The hospital has said this is necessary because of overcrowding - 33 people are reported to be waiting on beds with 27 on trolleys and six on wards.
Minister Varadkar said that the problem existed in other hospitals also and that a long term plan is required.
Mr Varadkar said: "The hospital itself has introduced a number of measures including postponing some elective admissions and discharging patients as much as they can.
"They're also getting support sent in from the HSE, with 19 step-down beds, additional home care packages and additional nursing home places to alleviate the pressures in the hospital.
"So I think we will see an alleviation in the next couple of days," he said.
At the Midland Regional Hospital in Mullingar 35 people were waiting on a bed earlier today, with 34 at University Hospital Limerick and 30 at St Vincent's Hospital in Dublin.
Beaumont Hospital said all non-urgent procedures have been cancelled or postponed until further notice and it is asking GPs not to refer new patients to the hospital's Emergency Department.
It said 14 cases were cancelled today, of which ten are day cases and four are planned procedures.
Beaumont said several factors have contributed to the difficulties in the Emergency Department including changes to cancer services across the region and recent service developments in the hospital which have drawn on its limited bed capacity.
A consultant in emergency medicine at Beaumont Hospital said that providing optimal care for patients is proving challenging because of overcrowding.
Abel Wakai told RTÉ's Six One news, that there are 98 long-stay-care patients at the hospital and that if there were better community supports or nursing homes for these patients, it would help issues.
He said that there are currently 23 admitted patients in the Emergency Department and that there are plans to open 17 extra ward beds this evening.
Mr Wakai said that 14 non-urgent surgical cases were cancelled today.
Five have been cancelled for tomorrow, with that number under review.
Beaumont Hospital went "off-call" for about four hours on Friday, during which time emergency cases were diverted to other hospitals.
The hospital, which is one of the largest teaching hospitals in Dublin, treats more than 50,000 patients annually in its Emergency Department and also provides cancer, neurosurgery and transplant services in the region.
Ambulance cases are still being accepted at the hospital.
Meanwhile, there were no major overcrowding issues reported this morning at the Emergency Department at Galway University Hospital.
Eight patients were on trolleys in the department by around midday.
The Irish Nurses and Midwives Organisation said this was an exception to the usual situation at the facility.
It said staff and services were put under severe pressure in recent days when a surge in patient numbers caused widespread difficulties.
Vomiting bug outbreak at MUH
Separately, Mercy University Hospital has cancelled all hospital visits with the exception of the children's ward for 24 hours due to an outbreak of the winter vomiting flu.
The hospital is seeking the public's cooperation with the restrictions, but will deal with exceptional cases on an individual basis.
