In her reply, Mrs May said she did not agree but thanked him for his work.
"I am also unpersuaded that our negotiating approach will not just lead to further demands for concessions", he said, concluding that his post required "an enthusiastic believer in your approach, and not merely a reluctant conscript".
In a letter to Davis, May disagreed with his characterization of her plans, saying the deal she seeks "will undoubtedly mean the returning of powers from Brussels to the United Kingdom".
She said she was "sorry" he was leaving but would "like to thank you warmly for everything you have done.to shape our departure from the EU".
In the Commons, Mrs May will acknowledge that there have been "robust views" around the Cabinet table and a "spirited national debate" since the 2016 referendum decision to leave the EU. There are now only two ministers remaining in the Department for Exiting the European Union.
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His role as Brexit Secretary was crucial to ensuring Britain leaves the European Union next year with what Mrs May described as the "best possible deal".
"That is not something that this country voted for; it's not what the Prime Minister promised..."
A Downing Street source said MPs will continue to be briefed on the plans, and officials will explain how it does not "breach our manifesto pledges, or our Brexit red lines".
The move, while not completely surprising, throws doubt on to how secure the government's Brexit strategy is.
The 100-page Brexit white paper, due this week, was the subject of a freakish ping pong between Dexeu and the Cabinet Office Europe unit, which repeatedly vetoed its language - and this was the reason for its delay, and the argument meant to be settled by Chequers.
Mr Davis and fellow Brexit backer foreign secretary Boris Johnson had both agreed to support Mrs May's proposal for a softer divorce than she had originally planned, and it seemed she had survived the storm.
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The Golden State Warriors have put themselves squarely in the conversation as one of the greatest teams of all-time. Golden State's Andre Iguodala was equally excited, tweeting, "Big fella!" One of the best players in the league.
"I'm a realist", Gove told the BBC on Sunday, admitting he didn't like everything about May's proposal.
"And I think without David Davis there, without his imprimatur, it will be very hard for them to get the support of Conservative MPs and therefore the prime minister would be well advised to reconsider them".
Writing in The Daily Telegraph, Mr Rees-Mogg said: "If the proposals are as they now appear, I will vote against them and others may well do the same".
"I would like to thank you warmly for everything you have done over the past two years as Secretary of State to shape our departure from the European Union", she said.
Peter Bone, a Eurosceptic MP allied to Mr Davis, told the BBC that he didn't see how the prime minister could get her Brexit plans through Parliament, and also that he couldn't see how she continue in her position if she didn't give into anger from the Conservative backbenches.
Insanely fast 5G OnePlus 7 smartphone incoming to smoke Samsung Galaxy S10
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