Three-quarters of the HSE's computer servers have now been unlocked after last month's cyber attack.
However, it will still be "many more weeks" before health services return to normal.
HSE chief executive Paul Reid will tell the Oireachtas Health Committee today that the ransonware attack on May 14th severely disabled a number of systems.
He says it has led to the complete shutdown of the HSE's computer network, and the systems are taking some time to restore.
However, around 75% of the computer servers, which were locked by the hackers, have now been decrypted.
Newstalk's technology correspondent Jess Kelly says the HSE isn't out of the woods yet.
He said: "We don't know how long it will take to do that final 25%.
"It can be a very arduous process. If we look at examples from Scotland and elsewhere around Europe... it can take months."
Mr Reid will tell the committee 70% of the HSE's end-user devices - such as laptops - are now available to staff.
However, the HSE's chief operations officer, Anne O'Connor, said outpatient appointments are still badly affected - with only about half going ahead.
She explained: "Sites have gradually been returning - we're at about 50-60% of our capacity now of general outpatients.
"Radiology outpatients is where we had our biggest problems, and we are still significantly behind in our radiology appointments."
She said work is still ongoing to restore some basic foundational systems, such as email and internet access.
However, she said there will continue to be disruption to services for many more weeks.
