"The PM said in her letter to the secretary of state that she didn't agree with his characterization of the position".
It won the backing of one other prominent Brexit campaigner.
In his letter, Mr Davis told Mrs May that "the current trend of policy and tactics" was making it "look less and less likely" that the United Kingdom would leave the customs union and single market.
- Davis led Britain's negotiations in Brussels on the terms of the European Union divorce, and the future relationship with the bloc.
Theresa May replied to Davis' letter, saying she did not agree "with your characterisation of the policy we agreed at Cabinet on Friday".
"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 added.
Davis' resignation was followed by that of Exiting the EU Minister Steve Baker.
While it throws the cards up in the air politically, investors have so far not been able to draw any firm conclusions on what it will mean for Britain's exit from the European Union.
Conservative MP Peter Bone hailed Mr Davis's resignation as a "principled and fearless decision", adding: "The PM's proposals for a Brexit in name only are not acceptable".
Opposition Labour leader Jeremy Corbyn said his departure showed May had not authority left and was "incapable of delivering Brexit".
The move, while not completely surprising, throws doubt on to how secure the government's Brexit strategy is.
Conservative MP Peter Bone said Mr Davis had "done the right thing", adding: "The PM's proposals for a Brexit in name only are not acceptable". "I won't be encouraging people to do that [challenge May]", he told BBC Radio 4.
David Davis had already expressed unease over the compromise plan.
The double resignation on Sunday has the potential to derail May's government and set in motion a chain of events that could lead to an attempt to oust her as prime minister.
She also said that Environment Secretary Michael Gove is the favourite to take on the vacant post.
Conservative MP and Remainer Anna Soubry did not refer directly to Mr Davis's resignation, but tweeted it was "not the time for egos, grandstanding and blind ideology".
The loss of her chief negotiator is a blow to the prime minister and comes as she prepares to face the House of Commons and then Tory MPs and peers on Monday to discuss her Brexit plans.
Meanwhile, some Remain-supporting politicians said the resignation was evidence of the need for a second referendum.
Veteran Tory Eurosceptic Sir Bill Cash told Sky that discussions were now being held as to whether Mrs May's plans amounted to a "proper Brexit". May's office confirmed that Davis had resigned but had no comment yet on the reasons. "You deserve the final say".
Davis did not urge other ministers to resign, saying he was in a unique position because the Brexit secretary's job is to sell the government's policy.
Denying that he wanted to unseat the prime minister, he said he would now "argue for being as firm as possible".
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