The HSE is asking people to consider all options and pathways available before attending emergency departments (EDs) as the health system faces pressure over the bank holiday weekend.
Patients attending EDs with non-life-threatening concerns are likely to experience delays.
The HSE added hospitals and community teams are continuing to identify patients who are suitable for discharge home or to community beds in order to ease the pressure in hospitals across the country.
HSE chief executive Bernard Gloster said: “We know that hospitals will experience pressure coming into Tuesday morning. Substantial work over the weekend has been of some benefit, but the position remains challenging.
“In as much as possible we want to reduce discomfort for the public and staff and part of that response lies in the use of all options.”
Where possible, people are being encouraged to attend injury units rather than EDs, particularly in the case of broken bones, dislocations, sprains, wounds, scalds and minor burns.
The public is also being urged to take caution on roads in the coming days, with a status yellow wind warning in place for Cork, Kerry, Galway, Clare, Mayo and Limerick.