Ireland's premier warned that future trade and customs restrictions would be detrimental to both the EU and the UK as he set out his vision for a "soft" Brexit.
Taoiseach Leo Varadkar proposed a bilateral EU/UK customs union and raised the possibility of the UK joining the European Free Trade Association (EFTA) after it exited the EU.
He said he would ideally like the UK to remain within the current customs union and single market structures but, if that did not happen, he suggested his alternative was "workable".
In response, the UK Government said it was committed to a "deep and special" future partnership with the EU that included "bold and ambitious" free trade and customs agreements.
Mr Varadkar outlined his ideas during a visit to Queen's University in Belfast, his first trip to Northern Ireland since replacing Enda Kenny in June.
Turning to the specific problem of the Irish border, he said a "unique solution" was needed.
Mr Varadkar again moved to dispel the suggestion that the Irish government favoured making the Irish Sea the EU/UK border.
In a message clearly directed at the pro-Brexit Democratic Unionists, he further claimed a "soft" Brexit could actually strengthen Northern Ireland's place in the United Kingdom.
In response to his remarks, DUP leader Arlene Foster said, while Brexit meant leaving both the customs union and single market, she wanted to find "practical solutions" to the border issues.
Sinn Fein President Gerry Adams welcomed the Taoiseach for offering a "very, very clear message" on Brexit.
Describing Brexit as the "challenge of this generation", Mr Varadkar repeated his hope that it would not ultimately happen, suggesting a second referendum might deliver a different outcome, but he said, if it did proceed, it would be in no one's interests to create trading barriers.
He urged continued UK membership of the Customs Union but said, in the absence of that, he would like to see a bilateral EU/UK customs union.
"After all, we have one with Turkey. Surely we can have one with the United Kingdom?," he said.
In regard to the single market, he suggested the UK could re-join the EFTA, like other non-EU countries such as Norway and Iceland.
"If the UK does not want to stay in the Single Market, perhaps it could enter into a deep Free Trade Agreement with the EU and re-join EFTA, of which it was a member prior to accession," he said.
"And if this cannot be agreed now, then perhaps we can have a transition period during which the UK stays in the single market and customs union while these things are worked out."
He again challenged Brexiteers to explain why a "hard" Brexit, with trade tariffs and customs restrictions, would benefit either the UK or Europe.
"If they can't come up with those solutions, well then maybe they might talk about mine, because the ones I have put forward are workable," he said.
Sinn Fein and the SDLP have demanded that Northern Ireland secures special designated EU status post-Brexit to reflect the difficulties that trading restrictions would pose at the Irish border.
Unionists are wary of the idea, as they claim it would differentiate Northern Ireland from the rest of the UK.
They claim it is being used by nationalists and republicans as a way to advance their united Ireland agenda.
Mr Varadkar said: "I would hope Unionist parties for example, who would be keen to preserve and protect the Union, would see how it is much easier to do that if in fact the United Kingdom stays in the customs union and stays in the single market because that takes away any need for any sort special arrangement or bespoke solution for Northern Ireland at all."
The UK government spokeswoman said: "We have been clear that we want a deep and special future partnership with the EU, including a bold and ambitious free trade agreement and a customs agreement.
"No-one wants a return to a hard border. We are clear that the border must be as seamless and frictionless as possible for trade, and that we must preserve the Common Travel Area between the UK and Ireland.
"That is why we are prioritising this issue in our negotiations and are pleased to have had constructive discussions with the European Commission on this already."
The Taoiseach said he was operating on the basis that Brexit would happen, but that he was still hopeful the UK would change its mind and remain in the EU.
He said that throughout political history, there was a precedence of people changing their minds.
"Of course I would hope the UK might think again and might decide to remain in the European Union, but I'm not operating on that basis," he said.
Relations between the DUP and Mr Varadkar have frayed in recent weeks, in no small part as a consequence of their very different views on Brexit.
After holding a meeting with the Taoiseach in Belfast later on Friday, Mrs Foster said the options for Brexit were "not binary", dismissing the characterisation of hard and soft exits.
"We were very clear with the Taoiseach that Northern Ireland as indeed the rest of the United Kingdom were leaving the European Union, that means exiting the customs union and the single market," she said.
"But, as we said before, we want to see the maximum access to the single market so we can make sure for businesses that there is continuing relationship with the European Union.
"We are leaving the European Union but we still want to do business very firmly with Europe and it is finding those practical solutions that we want to engage in.
"Not through megaphone diplomacy but actually through getting down to the nitty gritty for what's needed for Northern Ireland and the Republic of Ireland as well."
After holding a separate meeting with Mr Varadkar, Mr Adams welcomed his stance on Brexit.
"I criticised his predecessor (Enda Kenny) quite a few times and indeed the leader of Fianna Fail (Micheal Martin) because they seemed to be mesmerised by what the British were doing," he said.
"Now we have a very, very clear message.
"We have advocated special designated status.
"That doesn't infringe upon the constitutional position, it means the vote of the people here (56% Remain in EU referendum) is upheld and all their rights and entitlements."