The foreign secretary was accused of "backseat driving" by a fellow minister and rebuked by the statistics watchdog for his article outlining how "glorious" life will be outside the European Union.
But his 4,000-word essay also drew praise from eurosceptic members of the ruling Conservative party for his demand for a clean break with the EU, in particular on the fraught issue of financial payments.
Some saw it as an attempt to force May's hand ahead of Friday's speech in Florence, when she will give an update on her plans and the progress of negotiations with the EU.
"You could call it backseat driving," Home Secretary Amber Rudd, a senior cabinet minister who campaigned to stay in the EU, told BBC television on Sunday.
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May's grip on power remains fragile after losing her parliamentary majority in the June election.
Johnson, meanwhile, was a leading voice for Brexit in last year's referendum and has long been tipped for the top job.
A Downing Street spokeswoman sought to downplay the importance of his article, and stressed he had May's full confidence.
"The foreign secretary's views are well known. He was clear that he was united behind the prime minister's plan for Brexit," she said.
'Punctured the gloom'
Johnson has been silent on domestic issues for several months, but a number of newspaper articles last week suggested he was disgruntled with the progress of Brexit.
With questionable timing -- on Friday night, hours after a bomb attack in London -- he laid out the opportunities of Brexit with his usual flair in an article for the Daily Telegraph.
Johnson argued against paying for continued access to Europe's single market -- a possibility other ministers have left open.
He also drew criticism for reviving a hotly contested referendum campaign claim that Britain would regain £350 million a week to spend on public services once it stops paying into the EU budget.
The head of the independent UK Statistics Authority, David Norgrove, publicly rebuked Johnson for a "clear misuse of official statistics", saying the figure confused gross and net contributions.
But Eurosceptic Conservative lawmakers welcomed the article, with one, Jacob Rees-Mogg, saying Johnson was "loyally putting forward government policy... with panache".
Another, Nadine Dorries, wrote on Twitter: "The PM is not furious. It was a drum roll for her speech next week. It punctured the gloom."
'Party discord'
The row made headline news even as British authorities dealt with Friday's bombing, the fifth terror attack in six months, which injured 30 people.
"Party discord: Think many would agree we are not witnessing our finest hour, at a testing time when poise, purpose and unity are called for," tweeted junior defence minister Tobias Ellwood.
Tim Bale, professor of politics at Queen Mary University of London, said Johnson was "desperately concerned not to be forgotten.
"After all, he still wants to be leader".
"More immediately, he either hopes to show that Theresa May doesn't have the authority to sack him, thus confirming him as a threat, or that she will sack him, giving him a chance to act as the main alternative if and when things go badly for her," he told AFP.
Matthew d'Ancona, a columnist in The Guardian, added: "This is really about the prime minister, rather than Johnson himself.
"The ridiculous pretence that all is well in her administration has been decisively and brutally punctured, and cannot be restored with a straight face."