HSE boss Tony O'Brien says the organisation are doing everything they can to deal with the crisis gripping the country's emergency departments.
His comments come as figures released by the Irish Nurses and Midwifery Organisation show there are 2,000 closed beds in hospitals around the country.
The INMO also say that the number of patients on trolleys waiting for admission to hospital wards is around the same figure as yesterday, when the number passed 600 for the first time.
This number did not increase overnight.
Speaking on RTE's Morning Ireland programme earlier today, the HSE's Director General Tony O'Brien warned this number, "theoretically, could be higher next week".
This would be due to a number of external factors, such as an influenza type illness which would place further pressure on staff working in emergency departments
"The number could, theoretically, be higher next week," he told presenter Fran McNulty.
"The thing we're doing is designed to ensure that doesn't happen.
"I've looked at the trolley numbers three times a day every day for the last three years since I was in the Special Delivery Unit.
"I am very conscious that once a certain pressure builds up in emergency departments, it is not the easiest thing in the world to diffuse.
"The other thing is that the level of demand for services is not controllable.
"Doctors deal with everyone who comes through the door at this time of year.
"We're fortunate right now that we don't have a particularly high level of influenza type illness. "We don't have frost on the streets. if the situation changes, demand could increase.
"What I am telling you is that we're doing everything necessary to bring down the number and then try to keep it down but I can't give a guarantee," he added.
The Irish Nurses and Midwifery Organisation (INMO) says there are 2,000 closed beds in hospitals across the country.
The number of patients on trolleys waiting for admission into wards is broadly the same as yesterday where the figure passed 600 for the first time
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