Mr Davis was responsible for negotiating the UK's European Union withdrawal.
Davis, a sharp operator and a gut-instinct politician, was a "Leave" campaigner in the referendum on Britain's European Union membership.
Friday's agreement, which came after marathon talks at the prime minister's country retreat, would "make the supposed control by Parliament illusory rather than real", he added.
Davis was particularly critical of the proposal for a "common rulebook" to allow free trade in goods, saying this "hands control of large swathes of our economy to the European Union and is certainly not returning control of our laws in any real sense".
"It seems to me we are giving too much away, too easily, and that is a risky strategy at this time", he told BBC radio.
The resignation of Davis's deputy, Steve Baker, is a serious loss for May: Baker is widely respected among Brexit-supporting lawmakers.
Mr Davis also said that "the general direction of policy will leave us in at best a weak negotiating position, and possibly an inescapable one". "I would be front and centre in delivering this policy, explaining it to the House, persuading the House it is right, and then going out and delivering it with the European Union", he told the BBC's Today program on Monday morning.More news: Big crash for Hartley, Hamilton leads…
Will there now be a leadership challenge against May?.
May was scheduled to address all Tory parliamentarians at a meeting on Monday night. Sources close to Jacob Rees-Mogg have always said that he supports the prime minister, and appears to be urging colleagues not to do so....
She will face them at a meeting of the party later on Monday.
In order to trigger a challenge, MPs need to lodge a letter with the chair of the so-called 1922 committee of backbench MPs.
Is May's future on the brink?.
The Conservatives now have 316 members of parliament (MPs) so 48 of them would need to write such letters to challenge May.More news: America's first dogs came from Siberia, disappeared after Europeans arrived
"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".
More importantly for May's most anti-EU critics in the party, getting rid of May now would not fundamentally change the parliamentary arithmetic, which is now firmly in favour of a softer Brexit.
"It is now clearer than ever that Theresa May does not have the authority to negotiate for Britain or deliver a Brexit deal that protects jobs and the economy". His friends told the Daily Express that he was "extremely frustrated" with the Government's approach to Brexit.
"There's going to be a challenge nearly certainly in the next hours or days", Brooks said.
For many Conservative supporters of Brexit, though, May has sold out and they do not want her to lead the party into the next election, which is due on May 5, 2022.
However, even in that event it seems to me that the national interest requires a Secretary of State in my Department that is an enthusiastic believer in your approach, and not merely a reluctant conscript.More news: Kylie Jenner has removed all her lip filler
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