In a WhatsApp message to Conservative MPs, he suggested they were "some sinister band of imposters", according to Sky News.
A source, claiming to be a supporter of Johnson, said that moving him would go down "like a bucket of cold sick" with those who'd voted for Brexit.
A message sent by Boris Johnson to fellow Conservative MPs has since been leaked, in which he told MPs to "circle the wagons and turn fire on Jeremy Corbyn".
Claiming the Tories are "in all sorts of trouble" over Brexit, Ms Thornberry added: "It doesn't really matter who their leader is, they don't know where they are going".
'I heartily disagree with the sense, tone and spirit of what they are quoted as saying. "Whoever they are they do not speak for me".
James Airey, Leader of the Conservatives in Cumbria and the Parliamentary Candidate for Westmorland and Lonsdale at June's General Election, said: "In her speech yesterday, Theresa May reached out to a wide audience, just as she did in her inspiring speech on the steps of No.10 previous year, and we applaud her".
Many Tory MPs are understood to be furious about what they regard as Mr Johnson's disloyalty, setting out his own "red lines" on the Brexit negotiations in defiance of government policy, and want him removed.
Former justice minister and fellow Brexiteer Michael Gove also urged Leavers to rally behind May, tweeting: "Strong statement from PM on Brexit - let's be pragmatic over implementation to secure maximum freedom to diverge from European Union in end state".
"The Treasury seems unable to hear any voices except those that reinforce their preconceptions".
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Tory MP Nadine Dorries was even more direct, telling ITV's Peston on Sunday: 'If I were prime minister, the person I would be demoting or sacking would be Philip Hammond'.
She stressed it was "highly unlikely" that any new laws would be brought in during that period that hadn't already been discussed "and on which we would have been able to say whether they would be a rule that we would sign up to, or a rule that we would not wish to sign up to".
Eurosceptic Tory MPs turned on Hammond, saying he should be demoted instead for "deliberately trying to make Brexit negotiations hard".
"If that was just a problem for the Conservative Party I wouldn't be particularly bothered, but it's a massive problem for the country at the moment", the SNP politician added.
Defence Secretary Sir Michael Fallon insisted the Cabinet is united.
While this was less than the 48 needed to trigger a leadership contest, as was reported in The Week on Friday, the plotters had hoped to circumvent the powerful backbench 1922 Committee and appeal directly to the Prime Minister to set out a timetable for her departure.
But within hours, his allies began to rally round - saying that Boris could "just say no" to a new job, and warning that pro-Brexit voters need a champion at the top of the Government.
Britain's Foreign Secretary Boris Johnson.
However, a spokesman for the Prime Minister clarified on Monday that May has full confidence in Johnson, a media report states.