A Minister of State has said the HSE has spent the weekend retrieving data from back-up devices.
The extent of cyber attacks on the Department of Health and the Health Service Executive (HSE) will become clear as this week goes on.
Thousands of patients have had their appointments cancelled for the coming week, with urgent care prioritised.
A review of all IT systems within the Government is now believed to be taking place.
Minister of State for eGovernment, Ossian Smyth, told Newstalk Breakfast they will not be paying any ransom.
"I think there may have been a mistake made by the attackers because I think they previously attacked healthcare facilities in other countries that were private.
"Sometimes a private company thinks it's in their interests to pay a ransom - they work out that, in practice, it would be cheaper to pay up than to pay for the security.
"And that's not a calculation we'd make: we're a State and we don't pay a ransom - if we paid ransoms, we'd have people coming back".
Asked about concerns over personal information becoming public, he said paying a ransom would not change that.
"That risk of data being published doesn't get reduced by paying a ransom.
"The experience in the past of these criminal gangs is that you pay them a ransom and then they don't publish your data - but they sell it to somebody else.
"And then that person eventually exploits it and then publishes it.
"You're not dealing with people who are following some kind of code of business".
'No spread to other departments'
He said the HSE has already started retrieving information from back-up systems.
"What the HSE has been doing this weekend is they've been getting their information back from back-ups.
"We're not in a situation where we're under the control of these hackers, and that we're relying on them and that we need to get decryption keys - we're not doing that.
"And we're not paying them not to publish our data either.
"What they are doing is they've spent the weekend restoring the data, getting it back, getting their services back [and] turned on again.
"And you can see already that in many areas the disruption was really quite minimal".
Asked about vulnerability across other Government or State departments, Minister Smyth said there are no indications of this.
"The HSE has something called the NHN - the National Health Network - immediately all Government departments cut their connections to that as soon as that news came out on Friday morning.
"And other hospitals did as well.
"The indications that I've had, because the Office of the Government Chief Information Officer reports to me, is that there hasn't been any spread to other departments.
"The other departments... we've supplied them with a toolkit so that they can check whether there's any evidence of this.
"But from yesterday's meeting, I'm assured that there is no spread into other departments."
He added that these criminals targeted particularly the health sector "because they were under such pressure during the pandemic".
Anne O'Connor, Chief Operations Officer at the HSE, told Newstalk on Sunday: "The nature of this attack is that our data has been encrypted and possibly stolen, but we just don't know that bit of it yet".
"[The perpetrators] took the data and encrypted it, our data is encrypted, but they encrypt it and seek money to give us to code to release it back to us.
"From our perspective, we're looking at rebuilding using clean backup data."
Ms O'Connor said her focus is on getting the patient management systems and radiology systems back online again.
"All of our diagnostic capability in terms of radiology has gone, we are currently disconnecting machines after we have spent years developing an integrated system," she explained.
"The risk is, for example, if you have somebody coming into a hospital for anything, we have no capability to look back at previous tests or scans, we can't order lab tests or radiology electronically.
"So for anyone coming in, it's back to manual, handwritten notes."