Taoiseach Micheal Martin will discuss the different travel restrictions between Northern Ireland and the Republic at this week’s meeting of the North-South Ministerial Council.
The council, one of the bodies set up under the Belfast Agreement, will meet in Dublin on Friday for the first time since 2016.
Sinn Fein leader Mary Lou McDonald has accused Mr Martin of maintaining a “passive stance” in highlighting the need for an all-island approach when it comes to health.
She said: “We do it for animal health, why do we not do it for human health?
“Can I say to you, Taoiseach, that is your opportunity to bring your critique of the Northern position in terms of international travel and to debate that with your colleagues.
“Sinn Fein will support you in that. We need a single island system of protection as that is the only way we can get ahead of this virus.”
Mr Martin said the Republic of Ireland has stricter travel restrictions in place, with people advised to only visit an approved list of 15 countries, while Northern Ireland allows 58.
He said while the issue of travel restrictions will be discussed, there are challenges when it comes to adopting an all island approach.
“We do have to have a reality check in terms of what is possible and what is not possible and we need to be honest with people,” he said.
“I think I have to make the point because we have had a much stricter guidance in the Republic with regard to travel – stricter in terms of what is going on in the North at the moment.
“I think it important to recognise the dangers travel can present in terms of creating spikes on the island of Ireland. We have to work towards a joint approach in relation to that.”
Elsewhere, People Before Profit TD Richard Boyd Barrett, whose party has representatives on both sides of the border, said a united Ireland will not be possible due to the different health services.
“Why would anyone from the North want to be part of a united Ireland when we have a dysfunctional, two-tier health service,” he said.
“They won’t do it. We need a national public health service.”
Mr Boyd Barrett also called on the Taoiseach “to separate Church and State”.
He added: “Why on earth would people in the North join the State when 90% of our schools are controlled by the Catholic Church?”
Mr Martin said the Government has set up a “Shared Island” unit which will work towards a consensus on a shared island, but has ruled out a poll on a united Ireland.
He said he took Mr Boyd Barrett’s point in relation to the health service and added that one of the elements of the Shared Island unit will be to see how the two jurisdictions can use each other’s health services.
Mr Martin said Brexit will also feature highly on the meeting’s agenda.
He said: “We’re having the meeting for the first time in three-and-a-half years and I hope it will help us to create a structure that will help us deal with the undoubted difficulties that Brexit has brought about.
“We do need to navigate and manage the island in a post-Brexit situation.”