Tánaiste and Minister for Foreign Affairs Simon Coveney has said Ireland will never sign up to a treaty that will see a physical border re-emerge on the island of Ireland.
Speaking at a conference in Cork, Mr Coveney said any such deal would have a corrosive effect on the Good Friday Agreement and on trade on the island.
He also said he believes a no-deal Brexit is very unlikely because of the negativity of all other options.
Elsewhere, the Sinn Féin Vice President has said that the DUP does not speak for the people in Northern Ireland.
Michelle O'Neill was speaking in Brussels this afternoon after a meeting with Michel Barnier, the EU Chief Negotiator on Brexit.
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She said she had travelled to Brussels, along with the leaders of three other political parties (SDLP, the Alliance Party and the Green Party), to make sure that Mr Barnier heard the voice of the majority of citizens in the North.
Ms O'Neill said that Mr Barnier had listened intently to her concerns and she welcomed his firm commitment to the backstop.
She said she believes that Mr Barnier understands the Good Friday Agreement and the North's "special and unique" circumstances more than the British government.
When asked about the UK's suggestion that the Northern Ireland Assembly should approve any final backstop agreement, Ms O'Neill said that she would rule this out as it was never going to work.
She said that all four of the political parties who had travelled to Brussels today agreed because the Petition of Concern mechanism effectively gives a veto to those who want to use it.
She said she was sure that the DUP would use this mechanism to thwart any progress made in the Brexit negotiations and this was not acceptable.
She said it was too early for optimism as she did not know how the talks would end.
However she welcomed Mr Barnier's assessment that there would be clarity on the issue later this month.
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Earlier, the Tánaiste said he did not feel Ireland was at risk of being pressed to make concessions on the border in Brexit negotiations.
Speaking on RTÉ's Morning Ireland, Mr Coveney said: "I don't think we were ever in danger of that.
"We have worked hard for the last two years to build and maintain very strong solidarity with the Irish issues."
He said that there is "no country in the European Union that is questioning the importance of the Irish border issue".
He added: "I believe that Theresa May is absolutely committed to protecting Ireland through Brexit as well as obviously advocating for Britain's interests, and what I mean by that is protecting the Good Friday Agreement, and ensuring that the guarantees she has given that there will be no future border infrastructure on the island of Ireland will be followed through on."
The Tánaiste said the Government cannot rely on the Northern Ireland Assembly to sign off on any new regulatory checks that could form part of a potential Brexit deal.
A clause called the Petition of Concern could allow the Assembly to approve - or block - Brexit proposals relating to the border issue.
But Mr Coveney said that any agreement would have to be between the British government and the European Union, regardless of whether there is a devolved government in Northern Ireland.
"Everybody wants to have an assembly back up and running but we can't rely on that because we haven't had an assembly up and running now for over 20 months.
"So any agreements that are made and signed off on are between the British government and the European Union.
"And that will be the legal text of a treaty that will be fully operable whether or not there is devolved government functioning in Northern Ireland or not. So in other words, in all scenarios, Brexit needs to work," said Mr Coveney.
Petition of Concern
Agreement through the Northern Ireland Assembly is unique because of the Good Friday Agreement and because of a clause of what’s known as the Petition of Concern.
It was put in there, in some respects, to recognise the downtrodden minority factor. And basically it means that unless you have cross-community support for something, it doesn’t happen.
Let’s look at the numbers in the Assembly.
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The DUP is in a minority situation. The DUP has 28 Assembly seats in a 90-member Assembly. It could muster, in some situations, the backing of the Ulster Unionist Party - maybe not all of them, ten members - maximum 38. Maybe Jim Allister - 39 out of 90 - a minority.
On the other hand - looking across the table - Sinn Féin 27, SDLP ten, Alliance eight, Greens two - 49.
So you have 49 people in the Northern Ireland Assembly - more than a simple majority - 49 out of 90 who are in favour of remaining in the Customs Union - they didn’t want to leave the European Union.
So say for instance, you tried to bring in some of these regulatory barriers that needed the consent of the Northern Ireland Executive and the Assembly. What the DUP in a minority position could do is opt for this Petition of Concern handbrake.
To trigger that you need just 30 of the 90. Their own members and a few Ulster Unionists would give them that.
So in effect a minority position, using the Petition of Concern, could be a blocking mechanism.
UK will preserve integrity in any Brexit deal
The UK's integrity will be preserved as part of any Brexit deal and there will be no new regulatory barriers between Northern Ireland and the rest of the UK unless the province's executive agree, Britain's Brexit ministry.
"We will set out our alternative that preserves the integrity of the UK," the ministry said.
"And it will be in line with the commitments we made back in December - including the commitment that no new regulatory barriers should be created between Northern Ireland and the rest of the UK unless the Northern Ireland Executive and Assembly agree."
When asked when Brexit Secretary Dominic Raab would travel to Brussels, a spokesman said the schedule for any talks would be posted online.
European court fast-tracks Brexit reversal case hearing
The European Court of Justice will consider next month whether the UK can unilaterally withdraw its Article 50 Brexit letter.
It comes after Scotland's highest court said it would refer the question to the ECJ in Luxembourg.
The case has been brought by Jolyon Maugham QC and a cross-party group of politicians in Scotland.
Mr Maugham said a hearing would take place on 27 November.
Additional reporting: Tony Connelly, Reuters, Press Association
