Barnier said had told the British government that "the border issue will be one of my three priorities for the first phase of the negotiation", along with protection of European Union citizens' rights and the settlement of Britain's financial obligations to the EU.
Addressing a joint session of the two houses of the Irish parliament, Michel Barnier said a border that divides the island, and Ireland's economic and historical ties with the United Kingdom would be taken into account in the Brexit negotiations, which he will lead when they get under way later this year.
Then Mr Barnier will meet the Taoiseach Enda Kenny and the Minister for Foreign Affairs Charlie Flanagan in government buildings and the upcoming Brexit negotiations are top of the agenda.
It is an honour previously enjoyed by Nelson Mandela, Bill Clinton and Tony Blair.
This two-day trip will include a visit to the North and the border region, with the aim of getting a clearer vision of just how Brexit will affect Ireland.
Mr Barnier said: 'if we put things in the right order, if we negotiate with mutual respect, without any kind of aggressivity. if we are open to finding solutions, there is no reason why a strong Europe can not maintain a strong relationship with the United Kingdom'.
"We have consistently urged both sides to adopt a constructive approach to these negotiations, there is no point in having verbal wars before the negotiations ever begin", he said.
"We've heard a lot of talk on the media about it but nobody has actually come and said to us what is going to happen".
Barnier said returning to the "instability of the past" would be avoided and acknowledged that Ireland was in a "unique position" regarding the negotiations.
He called for "mutual respect" in negotiations, in an apparent reference to the diplomatic row caused by leaks following European Commission president Jean-Claude Juncker's Downing Street meeting with Theresa May. "And in Ireland's interest in particular", he added.
"We have to use our combined strength", he said, "and deliver solutions that benefit all member-states".
'But we will need the same ambition for our research and innovation networks and for the fight against climate change.