Boris Johnson has criticised the UK government's Brexit talks strategy, saying it lacks "guts" and suggested Donald Trump could do a better job.
The foreign secretary also took a swipe at Chancellor Philip Hammond, calling the Treasury "the heart of Remain", in comments to a private dinner.
He said the Brexit talks were heading for "meltdown" and Leave supporters may not get the deal they expected.
Theresa May said Mr Johnson "had strong views on Brexit but so do I".
Speaking in Canada, where she is attending the G7 summit, the prime minister refused to be drawn on whether the foreign secretary was undermining her, a day after a row with her Brexit Secretary David Davis.
She said the process of leaving the EU was "complex" but her focus was on getting the right deal for Britain and people should judge her on her record in the negotiations so far.
In a recording, obtained by Buzzfeed, Mr Johnson warns the UK could remain "locked in orbit around the EU" and claimed the Irish border issue - one of the main sticking points in talks with Brussels - had been allowed to dictate "the whole of our agenda".
"It's so small and there are so few firms that actually use that border regularly, it's just beyond belief that we're allowing the tail to wag the dog in this way," he said.
The foreign secretary was apparently speaking to around 20 people in a private room after an Institute of Directors reception on Wednesday night.
It follows a day of wrangling over the government's "backstop" plan in the event of no customs deal being agreed before Brexit.
Theresa May was forced to agree to a cut-off date of December 2021 for any interim arrangements after Brexit Secretary David Davis threatened to resign.
But speaking to reporters on route to the G7 summit in Canada, she twice refused to give a "cast-iron guarantee" that the end date would not slip beyond that.
And speaking in Brussels, the EU's chief negotiator Michel Barnier said the proposal could only apply to Northern Ireland, not the UK as a whole, and questioned whether temporary arrangements were acceptable, telling journalists "backstop means backstop".
In the leaked comments, Mr Johnson said the prime minister was "going to go into a phase where we are much more combative with Brussels".
He added: "You've got to face the fact there may now be a meltdown. OK? I don't want anybody to panic during the meltdown. No panic. Pro bono publico, no bloody panic. It's going to be all right in the end."
Brexit will be "irreversible" and will happen, Mr Johnson said, but the "risk is that it will not be the one we want".
He added: "Unless you make the change, unless you have the guts to go for the independent policy, you're never going to get the economic benefits of Brexit. You'll never get the political benefits of Brexit."
He was said to have described concerns over the border between Northern Ireland and the Irish Republic as "pure millennium bug stuff" and suggested Chancellor Philip Hammond's department was "basically the heart of Remain".
Speaking about the Treasury, he added: "They don't want any disruption of the economy. So they're sacrificing all the medium and long-term gains out of fear of short-term disruption."
In response, Mr Hammond said his "advice to colleagues" was to engage with the EU as his experience was "a collaborative approach is generally more productive than a confrontational approach".
But Brexit-supporting MPs backed Mr Johnson, Peter Bone saying Mrs May "probably agrees with him as well".
The talks, he said, were "being held back by Remain officials who are driving this thing" - suggesting they should all be removed and Brexit Secretary David Davis given a "free hand".
No 10 said there was "rigorous debate" about Brexit but its focus was on delivering the deal the public wanted.
Scotland's First Minister Nicola Sturgeon said Mr Johnson was "simply not fit for the high office he holds" while Irish leader Leo Varadkar said "when I want to know what the view of the British government is, I listen to the prime minister".
Labour MP Rupa Huq, who campaigns against a "hard" Brexit, said Mr Johnson had been "very dismissive" of the risks to Northern Ireland, treating it - in her words - as a "small country that nobody bothers about".
Mr Johnson was the keynote speaker at Conservative Way Forward's summer reception and took questions for more than an hour, according to Buzzfeed.
Asked about Donald Trump, he reportedly said he was "increasingly admiring" of the US President and was "more and more convinced that there is method in his madness".
"Imagine Trump doing Brexit," he added.
"He'd go in bloody hard... There'd be all sorts of breakdowns, all sorts of chaos. Everyone would think he'd gone mad. But actually you might get somewhere. It's a very, very good thought."