Health Service Executive Chief Paul Reid has said the ongoing impact of the cyber attack is "beyond comprehension" and it will take a few more weeks yet to fully restore the IT systems.
On 14 May, the HSE was forced to shut down all of its IT systems following a "significant" ransomware attack, which focused on accessing data stored on central servers.
Mr Reid said that efforts are continuing around the clock to rebuild services, in tandem with keeping the health service running.
Speaking on RTÉ's Morning Ireland, he said there has been gradual progress made in restoring some radiology services at the children's hospitals and in getting patient registration systems back in Temple Street.
It is hoped that this system will be restored today at Children's Health Ireland (CHI) at Crumlin, he added.
Mr Reid said the cyber attack will have a profound impact on hospital waiting lists.
He said efforts are under way to return outpatient services and elective care, which is back to 60% in some hospitals.
He said private hospitals are "very much" part of the solution.
Yesterday, Mr Reid said that of the HSE's 5,000 servers, 96% of them have been screened and protected, which he said has to be done before they can be restored.
Almost 50% of the HSE's devices have been screened and protected before restoring, he said.
Mr Reid said the HSE is continuing to monitor the "dark web" for patient information and data.