Cross-border work on improving the monitoring of quarantining international visitors is moving forward, Taoiseach Micheál Martin said.
Harmonising travel regimes across the UK and Ireland will be "challenging" but the threat posed by the pandemic means politicians also have to act quickly, he added.
He hosted a "constructive and warm" North South Ministerial Council meeting at Dublin Castle today with Stormont First Minister Arlene Foster and Deputy First Minister Michelle O'Neill.
Mr Martin said: "This is a vicious virus, it spreads like wildfire in certain settings.
"That is not just a phenomena on the island of Ireland but throughout the world."
Read more:
- Coronavirus, travel restrictions and Brexit discussed at North South Ministerial Council meeting
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International arrivals in Dublin airport can cross the border into Northern Ireland despite impediments to how visitors from Covid-19 high-risk countries are monitored for self-isolation compliance once they do so.
Stormont health minister Robin Swann held talks this afternoon with his opposite number in the Republic, Stephen Donnelly.
Mr Swann has raised major flaws surrounding enforcement and monitoring of quarantine after international passengers arrive at Dublin airport then cross the border into Northern Ireland.
Mr Martin added: "There are different jurisdictions with different chief medical officers who come forward with maybe nuanced advice.
"These are realities but both chief medical officers will be engaging on these issues.
"It is moving because we have seen what is happening in France, Germany and Spain.
"These numbers are moving on very significantly at a rapid pace."
At present visitors from Britain can travel through Northern Ireland and across the border into the Republic without quarantining.
Visitors from Britain and other countries not of a green list of low coronavirus risk are required to quarantine for two weeks on entering the Republic.
Northern Ireland residents who travel to the Republic do not have to quarantine, and vice versa.
A meeting of administrations in the UK and Ireland to discuss travel restrictions has been sought.
Northern Ireland and the Republic have driven down the rate of transmission of the virus over recent months.
Yesterday the Republic reported 85 new cases.
The Taoiseach added: "Relatively speaking north and south are managing this relatively well so far but it will take vigilance."
First Minister Ms Foster referenced recent outbreaks in England.
"In relation to international travel, there is a need for a discussion on the location of international travellers as they come through Dublin so as there is good sharing of information."
She said the meeting was "worthwhile and productive".
Deputy First Minister Michelle O'Neill said members of eight parties in both administrations had met today.
She added: "Our cooperation is more important than ever as we continue to respond to the biggest health emergency we have ever faced and when we reflect on the previous months, we must reflect on the fact that 2,320 people have died from Covid on this island alone."
Mr Martin added: "It was a warm meeting, it was a meeting in which a wide array of views were expressed. North-south co-operation is a key priority for our government.
"It was extensive and constructive and we had a particularly good conversation about Covid-19," he added.
Read more:
- Coronavirus, travel restrictions and Brexit discussed at North South Ministerial Council meeting
- Micheál Martin 'concerned' about spike in coronavirus cases
