The council, one of the bodies set up under the Belfast Agreement, is meeting in Dublin for the first time since 2016 and will involve ministers from both sides of the Irish Border.
Sinn Féin leader Mary Lou McDonald had 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 Féin 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.
Brexit
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.”
Meanwhile, Arlene Foster is expected to appear alongside Sinn Féin vice-president Michelle O’Neill in public today following the meeting.
Bobby Storey’s funeral is still under police investigation over potential breaches by mourners of social distancing rules.
Mrs Foster said: “I have always made it clear that we need to have the Executive working and need to continue to deal with Covid.
“We need to continue to focus on recovery, dealing with EU exit meetings.”
Mrs Foster had said her powersharing partner’s apology after attending the republican funeral “falls short”.
Trust between members of the Stormont coalition and Ms O’Neill’s credibility in delivering Covid-19 health messaging was damaged by the controversy over large crowds as the cortege passed through west Belfast, the DUP leader said.
Ms O’Neill has stood by her decision to go to the west Belfast service for the senior republican but did say sorry to families bereaved during lockdown for any hurt caused by scenes of hundreds of people lining the route.
Mrs Foster said the Covid-19 tracker phone app launched in Northern Ireland on Thursday would work in an inter-operable way with the Republic of Ireland and any brought forward by other UK administrations.
Self-isolation with Covid-19 symptoms or a positive test result has been increased from seven days to ten in the North.
