Former Foreign Secretary Mr Johnson claimed his Brexit dream "is dying" in his scathing resignation letter.
Davis resigned late Sunday, saying May's plan to maintain close trade and regulatory ties with the European Union gave "too much away, too easily".
"I can´t see more ministers resigning", Simon Usherwood, politics lecturer at the University of Surrey, told AFP.
Barnier said he had never been shown how Brexit provided added value when the world faced challenges ranging from terrorism and climate change to migration, poverty and financial instability.
Mrs May said she was "sorry - and a little surprised" by Mr Johnson's move after his apparent support on Friday.
Hunt had been health secretary, and is a leading government backer of a compromise "soft Brexit".
"The prime minister knows it's a proposal and not an end agreement".
Johnson said in his letter that May's plan to keep close economic ties with the bloc means Britain is heading for a "semi Brexit" that would leave Britain with the "status of a colony" of the EU.
Trump's strained visit with NATO, meeting with Putin
The NATO summit is likely to be dominated by Trump's insistence that member nations step up and pay more for their joint defence. U.S. doesn't have and won't have a better ally than EU.
The Sun, Britain's biggest-selling newspaper, said there had been "blunder after blunder" by May.
Like Mr Gove - who infamously made a rival bid for the leadership after the referendum - Mr Johnson has always been suspected of aiming to lead the party and be prime minister.
The government of British Prime Minister Theresa May has been plunged into turmoil with the resignation of two senior Cabinet ministers, exposing a deep and perilous split over her Brexit strategy. But within 48 hours Davis had quit and Johnson followed.
'As EU negotiator I will negotiate only with the British government... so our next negotiations will be Next Monday with the British delegation appointed by Mrs May'.
Less than nine months remain until Britain reduces the EU's membership on March 29, 2019. "I won't be encouraging people to do that, I think it's the wrong thing to do".
She took to the House of Commons today to detail her Brexit proposals amid the chaos. "Others don't have that same responsibility".
But don't worry: His real resignation letter was just more subtle with the clues.
Asked about the possibility of a vote of no confidence on Mrs May, he said: "I would firmly believe that she would win that".