Britain's commitment to maintaining a soft Irish border after Brexit is "much more than legally enforceable", David Davis has said.
The Brexit Secretary said the UK would seek to maintain a "frictionless, invisible" border between Northern Ireland and the Republic even if Friday's last-minute agreement to allow trade talks to start collapses in the event of a "no deal" Brexit.
His comment on Sunday that the plans were a "statement of intent" was branded "bizarre" by the Irish government, which insisted an agreement that the UK will have "full alignment" with the EU on issues that impact on Northern Ireland was "binding".
But Mr Davis claimed his words had been "completely twisted".
He told LBC Radio: "What I actually said yesterday in terms was we want to protect the peace process, want to protect Ireland from the impact of Brexit for them, and I said this was a statement of intent which was much more than just legally enforceable.
"Of course it's legally enforceable under the withdrawal agreement but even if that didn't happen for some reason, if something went wrong, we would still be seeking to provide a frictionless invisible border with Ireland."
Mr Davis went on: "What we're saying is this bit of it, the bit about the full alignment argument on the issues which affect the peace process in the Belfast Agreement, we would look to that anyway because one of our absolute underpinning aims is to ensure that Ireland and particularly the Northern Ireland peace process is not harmed.
"And what's most symbolic in that is the absence of a hard border, the absence of border posts and that sort of thing.
"And we are quite certain we can do that by technical and other means even if we end up without a deal with the European Union."
Asked why he said the soft Irish border deal was a statement of intent, Mr Davis replied: "Because it's more than legally enforceable.
"In the event that the withdrawal agreement doesn't happen then we would still be seeking to maintain an invisible border between Northern Ireland and Ireland, that was the point. I was making the point it was much more than just in the treaty, it's what we want to do anyway."
Mr Davis dismissed concerns that a soft border between the UK and EU on the island of Ireland could encourage people smuggling.
"That would be a very hard way to get into Britain, you'd have to be a fairly dumb people smuggler to come in that way," he said.
"Something like 50 million people go through the country every year - tourists and so on - you go to Heathrow, look at it, there's huge numbers of people, it's much simpler to come in and pretend you're a tourist than to take a sort of elliptical route like that."
The Brexit Secretary said the UK would have talks with the Irish government about sharing security data to ensure illegal immigrants do not exploit the soft border.
The spat between Dublin and London emerged as Mrs May was chairing the first Cabinet meeting on Monday since her pre-dawn dash to Brussels to agree a way forward with European Commission president Jean-Claude Juncker last week.
With some Tory Brexiteers expressing concern that the UK has agreed to pay a £39 billion exit bill, let the European Court of Justice have a legal role for a further eight years, and pledged the full alignment on Irish border issues, the PM is saying she has been consistent in her approach.
In a statement to the House of Commons on Monday, Mrs May is expected to say: "This is not about a hard or a soft Brexit.
"The arrangements we have agreed to reach the second phase of the talks are entirely consistent with the principles and objectives that I set out in my speeches in Florence and at Lancaster House.
"I know that some doubted we would reach this stage.
"Of course, nothing is agreed until everything is agreed.
"But there is, I believe, a new sense of optimism now in the talks and I fully hope and expect that we will confirm the arrangements I have set out today in the European Council later this week.
"In doing so we can move on to building the bold new economic and security relationships that can underpin the new deep and special partnership we all want to see.
"A partnership between the European Union and a sovereign United Kingdom that has taken control of its borders, money and laws once again."
Former Conservative party leader Iain Duncan Smith said that while Mrs May's agreement was "not ideal" it was an improvement in the state of the negotiations.
However he said the deal was a draft that "simply gets us through the first round".
Writing in the Daily Telegraph, the leading Brexiteer said: "Most importantly, though, all this can be torn up tomorrow, because 'nothing is agreed until everything is agreed'.
"This is in effect an indicative text, whose purpose is to get us to the next phase of discussions."
Labour's shadow Brexit secretary Sir Keir Starmer said Mrs May "cannot now be spooked by the extreme Brexiteers in her party".
"The agreement last week should be treated as binding and was expressly intended to be part of the Article 50 withdrawal agreement," he told the Guardian.
"Labour will not allow any rowing back on promises made that would put the union or the peace process at risk."
The remaining EU27 countries will decide at a Brussels summit later this week whether trade talks with the UK can finally begin.
Comments by Mr Davis that the UK would not pay its £39 billion exit bill unless it gets a trade deal are likely to have caused disquiet on the Continent.
European Commission spokesman Margaritis Schinas said that the joint report published last week by Mr Davis and EU Brexit negotiator Michel Barnier was "not legally binding".
But asked if it was therefore possible for either side to back down on it, he stressed that it was regarded in Brussels as "a deal between gentlemen" which was "fully backed and endorsed" by the UK Government.
He noted that Mrs May and Mr Juncker had shaken hands on it.
"Formally speaking, the joint report is not legally binding because it is not yet the Article 50 Withdrawal Agreement.
"But we see the joint report of Michel Barnier and David Davis as a deal between gentlemen and it is the clear understanding that it is fully backed and endorsed by the UK Government.
"President Juncker had a meeting with Prime Minister May last Friday morning to ascertain that this is precisely the case. They shook hands.
"It is now for the European Council on December 15 to decide if 'sufficient progress' has been made, allowing the negotiations to proceed to their second phase."
Mr Schinas said that last Friday's agreement had "removed a big barrier" to progress but confirmed that nothing would be finally settled until the Withdrawal Agreement was signed.
At the regular weekly meeting of Cabinet - held, unusually, on Monday - Mrs May thanked Mr Davis and officials for their work in the first phase of Brexit negotiations.
Mrs May told fellow ministers that the general feeling she had picked up from voters in her Maidenhead constituency over the weekend was that "we're on our way", the PM's official spokesman told a Westminster media briefing.
The phrase was used by the Daily Mail in its front-page coverage of the Brexit breakthrough on Saturday, which ran under the headline: "Rejoice! We're on our way".
But the spokesman insisted that the PM had not been quoting the newspaper but repeating a comment made to her by constituents.
Other Cabinet ministers reported having received "positive" responses to the development from both Remain and Leave voters.
Mrs May's spokesman confirmed that last Friday's document represented a political agreement and would not have legal status until the signing of the final Withdrawal Agreement.
He added: "These negotiations have been conducted in good faith throughout and I don't think there should be any doubt about the goodwill with which we approach them."