The Irish Government may cover the cost of European Health Insurance Cards (EHICs) for people in Northern Ireland after Brexit.
The plastic gives UK citizens access to state medical treatment while travelling in the EU.
A no-deal Brexit would invalidate the cards.
Irish foreign affairs minister Simon Coveney said: “When EU citizens travel across the EU they have health insurance cover.
“We are working and will ensure that we extend that right to Northern Ireland.
“That will involve passing legislation here and it will involve the Irish Government, if necessary, paying for that insurance cover for citizens in Northern Ireland.”
Mr Coveney addressed the Dail parliament in Dublin on Tuesday.