"I think [Prime Minister] Theresa [May] is going to go into a phase where we are much more combative with Brussels," he was recorded saying to Conservative activists at a dinner. "You've got to face the fact there may now be a meltdown. OK? I don't want anyone to panic during the meltdown. No panic. Pro bono publico, no bloody panic. It's all going to be all right in the end."
Johnson also played down what many see as one of the major stumbling blocks in Brexit negotiations: the question of whether new checks will be put in place on the border between Northern Ireland and Ireland, an EU member.
Johnson says there will be no hard Irish border
"It's so small and there are so few firms that actually use that border regularly. ... We're allowing the whole of our agenda to be dictated by this folly," he said.
The comments, made on Wednesday, were released on Thursday by BuzzFeed just hours after ministers reached a compromise on a backstop plan for the Irish border. The plan foresees the border remaining aligned with EU customs rules until a permanent new trade deal avoiding a physical border between Northern Ireland and the Republic of Ireland is negotiated.
EU officials have so far been skeptical about the plan.
May 'still has confidence' in Johnson
Johnson's remarks are likely to embarrass May, who is endeavoring to present her government as assertive and in control during the difficult negotiations.
After his comments were made public, a spokeswoman for the prime minister said on Friday only that May believed "that her Cabinet and her government are working hard to deliver on the will of the people and working hard to take back control of our money, laws and our borders."
Asked whether May had confidence in Johnson, she replied, "Of course."