The Health Service Executive (HSE) says a backlog of appointments due to Storm Ophelia could take a few days to clear.
It says there was "a significant impact" on the vast majority of health and social care services due to the weather conditions on Monday.
All outpatient appointments were cancelled due to the storm.
The conditions are expected to pass over Ireland during the night.
But the HSE says some disruption is likely "over the coming days" due to a number of factors - including road conditions, building damage, power outages and disruption to full staffing levels.
It also says some elective surgery will be cancelled on Tuesday.
In a statement, the HSE says: "We can expect a gradual return to normal services over the next few days.
"Due to cancelled appointments over the past 24 hours and a subsequent 'catch-up' period required, people can expect some delays in their appointments and discharges from hospitals over the next few days.
"In the event of a cancellation, people will be contacted by the relevant service.
Health Minister Simon Harris | File photos
"The safety of patients and clients travelling at this time is paramount. In the event that patients or clients deem it unsafe to travel for an appointment, the service concerned will reschedule this appointment as quickly as possible.
"Community services’ primary focus will be on dealing with the most vulnerable patients and clients in the first instance.
"Regarding Acute Hospital services, the intent is to restore all services over the coming days. It is anticipated that outpatient services will be fully provided tomorrow with a small number of exceptions."
But it says given the impact of the weather on the hospitals over the past number of hours, it will be necessary to cancel some elective surgery on Tuesday.
"Urgent procedures will be protected and these cases will be prioritised.
"Should any appointments be cancelled tomorrow, hospitals will be in contact with those affected."
Health Minister Simon Harris says: "Today has been a difficult and challenging one for our health services and I want to thank all of those who came to work today and went above and beyond.
"We do expect some continued disruption over the coming days but we can expect a gradual return to normal services and that is now our priority.
"The message for tomorrow is if you have an appointment turn up as planned, unless you hear otherwise. In the event of a cancellation, people will be contacted.
"People can expect some delays in their appointments and discharges from hospitals over the next few days."