Taoiseach Micheál Martin has said the Government made no payment for the decryption key which the HSE is using to try to restore its IT systems.
He said diplomatic channels were not used to secure it and it is unclear why it was given by the hackers.
Mr Martin said that getting the decryption key is good but does not take away from the enormous work that still lies ahead to rebuild the system overall.
He said that it remains the case that data could be dumped.
Mr Martin said that the injunction that the HSE secured is a strong one, which makes it a criminal act to reveal any data that has been illegally obtained from the HSE IT system.
He said the Government appreciated the collaboration and cooperation from major social media companies.
Over the weekend, experts will continue to assess the application of the decryption key.
He said that it is slow work, but progress is being made and asked people for patience.
Earlier, the National Cyber Security Agency validated the decryption key supplied online by the criminal gang which attacked the Department of Health and the HSE's computer systems and stole confidential personal and medical data.
They now need to remove the associated "flaws and bugs" and incorporate them into a decryption tool that is compatible with the HSE systems to safely restore the stolen data.
The agency along with IT specialists are testing and validating the key which is a complicated algorithm and is "highly flawed."
It is estimated that the gang spent hundreds of thousands of euro designing and inserting the ransomware and will be seeking some return through publishing the information on the darknet or selling it on to other criminals for extortion and blackmail.
However, specialists believe the High Court injunction on publishing the information has limited the criminal gang's options.
Today, a number of social media companies with headquarters in Ireland have responded to the High Court injunction secured by the HSE.
A Facebook spokesperson said the company was "aware of the court order and will act swiftly to remove content that is illegal, once we are aware of it".
A spokesperson from Twitter said it "complies with all properly scoped and valid legal requests, as per our law enforcement procedures".
While, Google said its search results were an index of content on the open web.
"We remove pages from our index in limited circumstances, including when required by law," a spokesperson said.
The NCSC and the private IT specialists contractors said they have not engaged at all with the criminal gang responsible who are being targeted by gardaí and law enforcement agencies in the US, the UK and Europe.
They are satisfied that this criminal gang knew that it had attacked a health service and that its crime would impact on sick, elderly and vulnerable people including children.
Digital notes left by the criminal gang were addressed to the HSE and investigators are satisfied the gang targeted the Health system and this was not "an accidental discharge."
All parties involved insist that no ransom has or will be paid by the Government, that no money has changed hands and that no agency, representative, or private individual, directly or by proxy has or will pay any ransom and that none will be paid and disguised in the fees paid to a commercial company.
Security specialists working to restore the systems have described the decision of the criminal gang to publicly release a decryption key as "highly unusual".
It is not clear why they did this publicly, they may be seeking to increase pressure for a ransom payment but may also be under pressure from political or criminal factions in their own country.
However, law enforcement officers say it is not possible to predict what the gang will do but the Government has decided not to engage with the organised crime group.
It cannot be seen to give credence or credibility to criminals or validate their business model.
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They have established it to be "a valid decryptor", "a binary solution" which they validated by programming it into a "sandbox" which is a safe cyber environment in which to 'open the key'.
IT specialists were able to then use it within that safe environment on a sample of the HSE's encrypted data, and discovered that the key decrypted the data.
However, while they now have the algorithm, the decryption code, they need to build "an engine" in order to be able to use the code to unlock the corrupted data.
"We have the cargo but we now have to build the truck" one specialist said.
The criminal gang inserted "a rolling encryption" into the HSE’s systems to capture the data but also pushed that encryption down through the entire system.
IT specialists say it is therefore a complicated task to unlock the data even with the algorithm code because the code changes or "reiterates" every time they go into the system and they must recommence at the exact same place.
They say it is a complex procedure which if not done carefully could corrupt the data.
The IT specialists also have to undo some of the protections that they put into the system to use the decryption key "a long string code".
As one specialist put it "we have to take reverse engines and take one step back to move five steps forward."
The NCSA and its private contractors are continuing to work 24 hours to avoid corrupting or losing data and to resolve the issue.
Officials say once the decryption key that can be used on the HSE systems has been built they can begin rolling it out online.
They can also put it on USB keys and send officials to hospitals and health clinics and use it to restore systems onsite, however they are cautioning that this will take some time and some systems will take longer to restore than others.
What systems are restored and when will be a matter for the HSE.
The Government is also continuing to insist it has not and will not pay a ransom to the cyber criminals.
The Minister for Justice described the attack as a heinous crime and said the criminals who carried it out have no regard for human life.
Speaking in Glaslough, Co Monaghan, Heather Humphreys said it is clear the criminals do not care that they have caused untold chaos in the Irish health service.
She also confirmed that she will be meeting with Garda Commissioner Drew Harris tomorrow to discuss the attack.
Additional reporting Paul Reynolds, Paul Cunningham and Tommy Meskill