Gardaí have said they are not aware of any data stolen from the HSE computer system having been posted online today.
Threats to publish the data purporting to come from the organised cyber crime group believed to be responsible for the cyber attack appeared online last week.
The Garda National Cyber Crime Bureau along with the National Cyber Security Centre, IT specialists and international law enforcement agencies are monitoring the 'darknet' and other underground online networks used by cyber criminals.
However, so far no data from the attack on the HSE appears to have been published.
Gardaí have said that information purporting to be stolen HSE data that appeared online last week could be genuine, but this has still not been verified. Much of the material was redacted.
They also say they believe that unsolicited and pre-recorded messages threatening the release of such data that some people have received are "opportunistic" and are not from criminals who have access to the stolen data.
Garda Headquarters today reiterated its advice to people who have reason to suspect they are victims of cyber related crime, particularly the recent criminal cyber attack of the HSE, to report this to their local garda station.
They have again warned people not to engage or provide any information if they are contacted by people claiming they have their personal details and/or looking for bank account details.
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Earlier, Taoiseach Micheál Martin had said there was "no great evidence yet of any mass dumping of data" in relation to the cyber attack.
Speaking on RTÉ's Today with Claire Byrne programme, Mr Martin said the situation is being monitored very closely.
"If anyone has any suspicions, if anybody comes across any data, if you see it don't share it", the Taoiseach said.
"Report it, that's the simple message we have - report it to the gardaí."
Mr Martin said progress is being made on restoring services, and the decryption key "is helping".
He said it is a "despicable act" to steal someone's health data, and the hackers may not have realised they were taking on a government or a health service.
"It is criminal, these are criminals who will seek to exploit this data", he said.
"But again, we've had very good cooperation with social media companies, who have been very proactive with the Government in relation to this and have agreed to shut down anything and take it down as quickly as they see anything."
Hospital systems are coming back following a cyber attack on the HSE and a decryption key provided last week is helping, Taoiseach Micheál Martin has said | Read more: https://t.co/9cZSC08loy pic.twitter.com/mgTraNjm8p— RTÉ News (@rtenews) May 24, 2021
Mr Martin said the system is "always vulnerable" to an attack and there is "no foolproof way" of resisting such an attack.
The budget for national cyber security was increased, he said, but he added that "we need to do more".
He said Poland was very helpful in the early phase of the attack because they had suffered something similar, as was the UK.
"It's not one country on its own," he said. "We would have regular collaboration with international partners and expertise as well."
Mr Martin said they will be investing more in the health service from an IT perspective.
He said he has been of the view for a long time that they must invest "far more" in the health system from a digital and electronic perspective.
"And we've been too slow at that," he said.
"We can modernise our health service far more effectively, and it's an aim of mine and the Government to do that, and to use every available means at our disposal to modernise our health service from a digital perspective.
"I think we're making progress and I think the Covid experience will accelerate that."
The hackers, believed to be a Russian crime group, have been holding onto sensitive information for more than ten days now.
The disruption has resulted in thousands of appointments being cancelled since the ransomware attack.
Chief Executive of the HSE Paul Reid has said that good progress was being made to restore some of the national systems, with the deployment of a new version of the decryption key provided by the gang on Thursday.