The Health Service Executive (HSE) says that staff payroll will proceed this week but they may see some discrepancies.
In a statement, the HSE said: "Some issues could arise such as variations between what some staff are due to be paid and what they receive"
They said, however, that there has been "no impact" to payments due to more than 100,000 staff members since the recent ransomware attack.
The HSE said it is a "key priority" for them and any issues will be rectified in the coming weeks.
Earlier, Health Minister Stephen Donnelly confirmed that the HSE payment system is down as a result of the attack.
He said getting it back up and running to ensure HSE staff are paid is now “an absolute priority”.
He also confirmed that some of the 146,000 people working in the HSE are due to be paid on Thursday.
The HSE has said that contingency arrangements are already being actively worked on to mitigate any risk to payments that are due to staff later next week. At this stage, it says it is too early to say whether the HSE will need to use those contingency arrangements.
The health minister described the cyberattack on the HSE as “an attack on the Irish people, the health system and patients and their families”.
The individual reports being reported in the media were “heartbreaking” he told RTÉ radio’s News at One.
Some progress was being made in radiation and oncology services he said, but it would take weeks to rebuild the technology network.
Over the weekend tech teams had rebuilt the base layer of the computer network.
The HSE was working with the National Cyber Security Centre and the gardaí along with technical and cybersecurity experts. The HSE network was being checked system by system, server by server, to see what had been compromised, he said.
The minister said that there were extensive backups and a lot of medical files had not been compromised.
Postings of heavily redacted material were being examined and the gardaí were looking at this issue.
“We have no verification that what has been posted is real data. We are awaiting details to know if sensitive information has been released.”
Mr Donnelly said that progress was being made in priority areas and that many important services were running, the ambulance service was operating, contact tracing was running and the vaccine programme was running “full speed ahead”
When asked if the ransom was going to be paid, the minister said that was a matter for Justice.
On being asked about the timeline for discovery of the cyberattack, the minister said: “We found out on Thursday that there was an attack on the Department of Health. I was informed early Friday morning.”
The Department of Health communicated with the National Cyber Security team which was the protocol. The technical advice was that the attack on the Department of Health “didn’t detonate”.
Earlier, the HSE’s chief clinical officer, Dr Colm Henry, has said that contingency plans are in place for staff to be paid this week, but that the priority is getting key diagnostic services up and running as soon as possible.
All of the HSE’s computer systems had to be closed down because of the cyberattack, he told RTÉ's.
It was hoped that a contingency plan would be in place by Thursday of this week so that staff could be paid, but there was no guarantee that the contingency plan would be in place by Thursday.
There was only so much that could be asked of clinical teams, he added. It was hoped that the diagnostic information systems that were key could be restored quickly. The focus would be on those services this week.
“This cyberattack has had a profound impact on the HSE,” he said. So much of modern medicine was reliant on technology, particularly radiology and diagnostics, he added.
“We were left with no option but to close down the system to protect the 2,000 patient-facing devices and 80,000 devices (computers) in the HSE," he explained.
All clinical teams were being urged to order the absolute minimum of such services unless it was an emergency.
The priority for the HSE was to re-establish the clinical system as quickly as possible.
The voluntary hospitals, which operate using a separate system, were being utilised for key services, he said.
In hospitals, there were the same teams with the same expertise, but they were having to deliver care in a “painstaking” way to ensure there were no mistakes.
Earlier on Newstalk, emergency medicine consultant at Sligo University Hospital and Communications Officer for the Irish Association for Emergency Medicine, Dr Fergal Hickey said that they were working with one hand tied behind their back as they had no access to patients’ previous information or scans.
"We are doing this partly blind," he said.
Dr Henry warned that the re-establishment of the service could take “a considerable period of time” and the disruption to the system could continue for the coming weeks.