There "will not be a hard border" on the island of Ireland in the wake of the UK's withdrawal from the EU, the taoiseach (prime minister) has said.
Enda Kenny was speaking at a specially convened meeting of the British-Irish Council (BIC) to discuss the implications of Brexit on Friday.
He said: "We do not want to see a European border internally on the island of Ireland.
"There will not be a hard border from Dundalk to Derry."
The Common Travel Area allows people to move between Northern Ireland and the Republic of Ireland without passport checks.
But Northern Ireland Deputy First Minister said on Friday that he could not see how that arrangement could continue after a Brexit.
"The economic implications for us in a withdrawal from the European Union are very profound, costing us over a period of ten years anything in the region of £7-8bn and possibly even more," Mr McGuinness told a press conference.
"There is alarm in the north of Ireland among the business community, among the community and voluntary sector, among our universities, among our agri-food industry and there is grave concern about the prospect that whatever is said about the common travel area being protected.
"It's very difficult to see how it can be protected in the aftermath of the debate that was held mostly in England around the whole issue of immigration and which effectively won that vote for the racists within UKIP and the loony, right-wing of the Tory party."
First Minister Arlene Foster said suggestions there could be a poll on Irish unity following the UK vote to leave the European Union were "not helpful".
"There have then been denials from Micheál Martin and people like that to say that actually they weren't calling for a border poll, they were just thinking about it in a different context," she said.
"That's all very well at summer schools and whatever - I have to deal with reality, I have to be prepared for the people of Northern Ireland moving forward in this new era."
Mr Kenny said the Irish government would play an important role in the Brexit negotiations and would "make the strongest presentation for continued support for Northern Ireland".
"I will argue that very strongly at the European Council," he added.
Earlier this week, he said Brexit talks would need to consider the possibility of a referendum on reuniting Ireland.
But on Friday, he said a poll "is not going to arise now or in the medium term, or may not arise for a very long time, if ever."