"Productive cabinet meeting this morning - looking ahead to a busy week", May said on Twitter, as the resignations of Johnson and Davis sent shockwaves through Westminster and fuelled speculation that the turmoil could eventually topple her.
And former Conservative leader William Hague warned party rebels that voting against the Prime Minister's final deal could result in Brexit being indefinitely delayed or halted altogether.
Labour leader Jeremy Corbyn said: "David Davis resigning at such a crucial time shows @Theresa_May has no authority left and is incapable of delivering Brexit". In contrast to his predecessor, Hunt voted to remain in the bloc in the 2016 referendum.
The Sun, Britain's most popular paper, said Trump's comments were a new blow for Prime Minister Theresa May, who has faced two high-profile resignations from her cabinet and a rebellion by Brexit hardliners this week.
Tánaiste Simon Coveney has said that this has been a good week for Brexit despite the resignations that followed the publication of Theresa May's Chequers proposals.
Johnson said that at a meeting of the cabinet to decide the plan on Friday, he had accepted that "my side of the argument were too few to prevail".
Jacob Rees-Mogg, who leads the European Research Group of Tory MPs, said the amendment would "put into law the government's often stated position that Northern Ireland should be treated the same way as the rest of the country", and "ensure reciprocity of customs collection, and treating the United Kingdom and EU as equals".
This last would likely be unacceptable to Brussels, thus killing May's plan, but Rees-Mogg told AFP his aim was only "to help the government stick to some of its earlier promises".
"We must have collective responsibility".
He added: "Since I can not in all conscience champion these proposals, I have sadly concluded that I must go".
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"I don't think it's central to Foreign Secretary, but there you are".
The Brexit Secretary was understood to have serious reservations about both the plan and whether it could be acceptable to Brussels following the Chequers summit, but was absent from the television studios in the aftermath of the talks. Together with a customs partnership (which would require the U.K.to collect tariffs on the EU's behalf), this could remove the need for a physical border between Ireland and Northern Ireland - avoiding one of the greatest dangers aroused by this ill-conceived project - and allow close-to-frictionless trade in goods between Britain and Europe.
Speaking to Today, Ms Jenkyns said Mrs May's time was up as Prime Minister and she wanted a Brexiteer to lead the country.
Sir Graham refused to say whether he had received any such letters. The plans laid out in a 98-page government paper give Britain's most detailed answer yet to the question of what will replace it.
Senior backbencher Bernard Jenkin said there had been a "massive haemorrhage of trust" in Mrs May.
Asked if Brexiteers needed to put the PM's future to a vote of the Conservative party, he replied "it may well come that".
Asked if he was planning to quit, environment Secretary Michael Gove said "absolutely not".
The Kremlin said it hoped for an improvement in ties following the departure of Johnson, who had angered Moscow with his vociferous accusations over the poisoning with a nerve agent of a Russian spy on English soil in March. "It should be a chance to do things differently", adding "that dream is dying, suffocated by needless self-doubt".
"We do have a lot of allies, but we can't be taken advantage of", he said.