The Justice Minister has said she is "not aware" of personal data linked to the HSE cyber hack being published online.
The Cabinet is meeting on Tuesday morning, with the hacking of HSE computer systems, dubbed the "most significant cybercrime attack on the Irish state", top of the agenda.
The Government has rejected ransom demands from the crime gang responsible, and has focused on restoring all medical services as quickly as possible.
But there are concerns that if ransom demands are not met, personal data belonging to thousands of patients could be sold online.
Speaking before the Cabinet meeting, Justice Minister Heather Humphreys said: "We're working with our international partners, and if any data does appear we will deal with that.
"There's a lot of experience on this internationally, we're getting a lot of co-operation."
The minister met Garda Commissioner Drew Harris and officials from the National Cyber Security Centre (NCSC) on Monday, where she was told of the ongoing impact of the attack, as well as the technical responses deployed and work to recover the HSE's IT systems.
She said: "The NCSC are working, the Gardaí are working with their international partners as well.
Taoiseach Micheal Martin told RTÉ ahead of the Cabinet meeting that the priority is to restore medical services as quickly as possible.
"We're going to do everything we possibly can to restore services for people in this situation, particularly the most urgent services that people require," he said.
"The NCSC has been flat out since the weekend, working first of all to respond to the threat. But also to rebuild and get services back as quick as we possibly can."
The impact of the attack on services is expected to last throughout this week and beyond, with thousands of patients facing cancelled appointments and delays.
Private and voluntary hospitals will be brought on board to ease the burden, with "alternative processes" to be put in place for urgent cancer care needs.
The national co-ordinator of the General Practice Information Technology group, Dr Conor O'Shea, has said that the majority of GP services will remain up and running.
He told RTÉ's Morning Ireland: "Most GPs will be working pretty much as normal. So if you ring your GP this morning you will get much the same service that you did last Tuesday.
He said the process for sending prescriptions remains secure and has been unaffected.
However, he said urgent care needs would be prioritised, but routine check-ups will suffer.
"If there's anything urgent we can still get the appropriate referrals made, either through A&E or we have access to urgent diagnostics. But we've been asked to hold back on the non-urgent stuff," he said.
"That's the gap in the middle. Day-to-day stuff we can carry on as normal. Urgent stuff we can also carry on pretty well as normal, in terms of referrals to A&E and getting urgent tests done.
"But because of the effect on the diagnostic services, that more routine check-up stuff may be delayed for a period of time."
People seeking tests for Covid-19 are being asked to use walk-in testing centres across the country.