Taoiseach Micheál Martin has said it will "take some days" to assess the impact of the cyber attack on the Health Service Executive's IT system.
Speaking during a press conference this evening, Mr Martin said he has been fully briefed on the issue, adding: "We have the people and systems in place to deal with this."
He said the impact on services was something that has to be dealt with in a methodical way, and that an assessment was under way as to the impact, which he was said was the right thing to do.
"What's important is people cooperate with the HSE," he said, adding that emergency services are open, and the vaccine programme continues uninterrupted.
"We're very clear we will not be paying any ransom or engaging in any of that sort of stuff," he said, adding that the issue is being dealt with in a way that is in accordance with the advice of cyber security experts.
'We're very clear we will not be paying any ransom or engaging in any of that sort of stuff' Taoiseach @MichealMartinTD says of the ransomware attack on the HSE | Live blog: https://t.co/itscpwqdS7 pic.twitter.com/Pl4A4JNOST— RTÉ News (@rtenews) May 14, 2021
Earlier, the Minister of State for eGovernment Ossian Smyth said the cyber attack on HSE computer systems was "possibly the most significant cybercrime attack on the Irish State".
Speaking on RTÉ's News at One, Mr Smyth said the attack "goes right to the core of the HSE's system" but it is "not espionage".
The HSE has said that following an initial assessment the randsomware "is a variant of the Conti virus that our security providers had not seen before".
It said "a ransom has been sought and will not be paid in line with state policy".
It added: "The HSE is working with our partners in the National Cyber Security Centre and a range of our cyber security providers to rectify this issue. We will continue to work through this over the weekend."
Mr Smyth said that it was "an international attack" involving "cyber criminal gangs, looking for money".
"What they're attempting to do is to encrypt and lock away our data, and then to try to ransom it back to us for money."
Mr Smyth said the Government is "deploying everything" in response to this. "It's widespread. It is very significant, and possibly the most significant cybercrime attack on the Irish State.
"We are deploying everything to respond to this, and the way that's working is, for starters, it's a criminal investigation.
"So the Garda National Cyber Crime Bureau is involved, and also we brought in a world-class cyber security company for assistance," he said.
The HSE's Chief Executive Paul Reid has said the response from the Irish State and the HSE is that they do not engage in paying ransoms to international criminal organisations.
On RTÉ's Six One, he described the breach as a highly sophisticated ransomware attack by criminal elements which sent a message to a server to effectively begin the process of seeking a ransom.
Mr Reid said precautionary actions have been taking place all day to protect the HSE's IT systems and assessments are being made on each of its national and local systems to understand what has been accessed.
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The National Cyber Security Centre (NCSC) has said the HSE became aware of a significant ransomware attack on some of its systems overnight and the NCSC was informed of the issue and immediately activated its crisis response plan.
In a statement, the NCSC said it is intensively engaging with the HSE and deploying its resources to fully support the HSE in identifying the affected systems and to bring all systems back online.
The NCSC said it is also working with the HSE to identify the technical details of the malware used in the incident and will issue an advisory later to share these details.
The NCSC is also engaging with EU and other international partners to share information on the incident and to ensure that the HSE has immediate access to international cyber supports.
The Office of the Government Chief Information Officer (OGCIO) has said it is providing support to the HSE and as a precaution has closed any entry points between the HSE IT infrastructure and the Government Network.
While not directly responsible for the HSE, it does provide IT services/support and security to a range of Government bodies.
In a statement, it said infrastructure teams in OGCIO have been investigating and monitoring networks for any evidence of cyber-attacks.
They have not found any unusual or suspicious activity or any warnings from our monitoring tools. They are continuing to investigate the potential threat but there is no evidence of any breach.
The NCSC is also engaging intensively with the HSE and the OGCIO in a coordinated response to identifying the systems that have been affected with the aim of bringing all systems back online as soon as it is safe and prudent to do so.
Mr Smyth has said that the cyber attack on the HSE is "the one that got through", adding that there is a "constant bombardment" on State data.
"These types of attacks happen all the time, so that people are aware. State agencies are under constant attack, and what the National Cyber Security Center does is that they provide advice and defenses to 150 different parts of the State.
"It is just a constant bombardment. This is the one that got through."
Mr Smyth said there will be a "gradual reopening" of services as the NCSC deems that it is safe.
"What they (NCSC) are doing now is going through the network, and step-by-step, they are clearing through each section, each subunit of the network, and when it's safe, they're reopening.
"And what we will see is a gradual reopening of services, as the network is brought back online, but that will continue throughout the weekend, and possibly longer."
The minister said that "absolutely every resource" will be put into finding those responsible for the cyber attack and there will be a detailed criminal investigation.
"We will certainly find what the vulnerability was and clear that. But it is difficult to pursue people internationally but we will certainly try to make sure that its not worth their while."