Minister for Foreign Affairs Simon Coveney has rejected the idea that the DUP should have a veto on the British government's Brexit negotiations, as they approach the critical summit of EU leaders in December.
The minister also suggested that if Britain cannot remain inside the EU customs union and single market, then another solution had to be found.
Speaking at a meeting of EU foreign ministers in Brussels, Mr Coveney said: "I don't accept that the options should be limited on the basis of the political arithmetic in the House of Commons.
"That is not how a decision as fundamental and as important to Ireland's future and Britain's future should be made."
The DUP are currently ensuring the survival of British Prime Minister Theresa May's government thanks to a confidence and supply agreement reached during the summer.
"I don't think that the solutions for the permanent new relationship between Britain and Ireland and Britain and the EU should be subject to [a veto from] one political party of any hue, and their view.
"Lots of parties on the island of Ireland have a view here, and I think we need to try to take all of those views on board. Of course we listen to the DUP, but we listen to other parties too in Northern Ireland, and we listen to all the parties in opposition and in government in Ireland, which is what we're trying to do with the stakeholders consultations."
Mr Coveney rejected the notion that British negotiators were taken by surprise by the internal paper circulated by the EU's Brexit Task Force last week, which suggested that Northern Ireland should remain in the customs union and single market, or at least be bound by their regulatory frameworks.
"I don't believe the British negotiating team was overly surprised by the Task Force paper, even though that seems to be the media coverage in Britain.
"Anybody whose been following this process knows that Ireland has been consistent and stubborn and strong on the border issue because it's so important to the functioning of the island of Ireland; linked to a peace process, linked to normal commerce, and the movement of goods, services, livestock, people.
"We will continue to be firm and consistent on this issue. I know it's a difficult issue politically for the British negotiating team, but Brexit poses difficult choices. My job is to make sure Ireland's interests are represented."
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Mr Coveney said that if it were not possible for Britain to stay in the customs union and single market, then all sides would have to design a solution that allows North South co-operation to function.
"That's why we are asking for a rethink, and for more progress and clarity on this issue before December," he said.
He would not be drawn on what those solutions would look like, saying they were for the EU and British negotiating teams.
"Britain and Ireland, working through the structures that involve the EU Task Force, have to find a way forward that not only Britain can live with but that Ireland can live with too," he said.
"If Northern Ireland goes a different direction from a regulatory point of view, then you create unfair playing fields, which on the back of that there is going to have to be systems of checks and balances, and inspections to ensure standards."
At today's meeting of defence and foreign ministers, 23 member states signed an agreement on greater security and defence cooperation, known as Permanent Structured Cooperation.
Ireland has yet to sign up to the pact as it requires both Cabinet and Dáil approval.
Mr Coveney said: "In principle we're supportive. This does not undermine in anyway Ireland's neutrality. It's very consistent with the Lisbon Treaty which Ireland voted for.
"Really what this is about is enhanced cooperation for security within the European Union. But it's on a voluntary basis, on a case by case basis."
