There are concerns hackers could publish patient’s confidential information online.
Investigations are continuing into the extent of the cyber-attacks on the HSE and the Department of Health.
Thousands of appointments have been cancelled as a result, with urgent care prioritised.
The Government says it won’t be paying the ransom as it would leave the country open to further attacks.
Junior Minister Ossian Smyth, doesn’t believe it would stop the hackers publishing confidential information in any case.
"The fact is 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 the ransom, they don't publish your data but they sell it to somebody else, and that person exploits and and publishes it.
"You're not dealing with people who follow some kind of code of business."
