The Government has said that it is demanding "special status" for Northern Ireland after Brexit.
Minister for Foreign Affairs Simon Coveney has dismissed "language coming from London" in recent days that technology alone - cameras and online permits - could bypass the need for border posts.
Mr Coveney, who met with EU chief Brexit negotiator Michel Barnier during the week, said an unprecedented "political solution" was needed to keep the status quo and an effectively invisible frontier.
"What we are insisting on achieving is a special status for Northern Ireland that allows the interaction on this island, as is currently the case, to be maintained," he said.
"It is not so much about a soft or hard border, it is about an invisible border effectively, that you don't notice as you cross it.
"To achieve that, we need to draw up a political solution here as well as technical and practical one, which doesn't really have any precedent in the European Union."
Mr Coveney said the solution would have to respect the territorial integrity of Northern Ireland within the United Kingdom.
It would also have to make sure it did not create a back door to entering the European single market, he added.
"This is not going to be a straightforward problem to solve," he said.
Mr Coveney also said it is not satisfactory that in the absence of a devolved government, the population of Northern Ireland will have to rely on others to make their case on Brexit.
Speaking at the launch of the Joint Oireachtas Committee's launch of the impact of Brexit on the Good Friday Agreement, Mr Coveney said a big element of the efforts to get the Stormont Assembly back up and running next week is a realisation that there are negotiations going on in London and Brussels.
Meanwhile Sinn Féin spokesman Conor Murphy said time was running out to agree a deal in Northern Ireland before the deadline next week.
He said: "The governments have said now that the actual deadline for these talks is on the 27 of June, next Tuesday. And thus far we have not seen, as the British government and the DUP have been distracted with their other business, we haven’t seen the level of engagement that is required here.
"So, we are seriously concerned given the timeframe we are operating in; given the lack of any visibility in terms of the deal that is being negotiated by the DUP and the British government, that time is fast running out on this process."