Davis also told parliament the government can not get a good deal with the European Union if its hands are tied in negotiations by a vote that would give MPs the power to force her government to go back to the negotiating table if they reject a Brexit deal.
The British government has narrowly defeated a bid to give lawmakers more power over how the United Kingdom leaves the European Union - but only after offering concessions to a rebellious House of Commons.
In a full statement later posted on his website, Lee said his resignation was a protest against the government's attempts to limit the role of MPs in shaping what sort of Brexit Britain will have.
Compared to the government's proposal, this is a shorter time to respond, and gives parliament a vote to approve the response.
The government averted defeat Tuesday by promising that Parliament would get more say over the U.K. -EU divorce deal.
Earlier, Mrs May was hit by the resignation of justice minister Phillip Lee, who quit the Government live on stage during a speech in London in order to be able to back Mr Grieve's amendment.
On Wednesday, votes on whether to remain a member of the European Economic Area, which hands countries single market access in return for accepting the free movement of people, goods, services and capital, may expose the deep divisions in the main opposition Labour Party.
The Government's compromise is that a minister would come to the House within 28 days of a deal being rejected to tell MPs what will happen next, but an amendment tabled by former attorney general Dominic Grieve would insist on a binding Commons motion.
The Labour Party's Chuka Umunna, who backed staying in the European Union, welcomed the concession as the end of the government threatening to allow Britain to crash out of the European Union without a deal.
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The announcement caught not only allies Japan and South Korea off guard, it also took the U.S. military command in the South, U.S. President Donald Trump became the first sitting US president to meet with a North Korean head of state on Tuesday.
Brexit secretary David Davis urged lawmakers to "respect the result of the referendum" that approved the withdrawal.
The government says lawmakers should be offered a choice only between its final deal and no deal at all.
Parliament will vote Tuesday on a key piece of legislation, the E.U. Withdrawal bill, that would transfer European Union laws now on British books into British law after Brexit. But how much of the proposed amendment has actually been accepted by the government?
They were also told the first two parts of Grieve's amendment - including that MPs will have a veto on what do to if an agreement can't be reached by 30 November - would be considered with a view to being tabled to the Lords.
"If the PM goes back on that there will be no agreed amendment that I can support #sortitplease", leading pro-European lawmaker Anna Soubry tweeted.
These should be interesting discussion indeed as, although she had made concessions, May has also said that she will not allow MPs to tie her hands in the Brexit negotiations.
Speaking to City leaders, John McDonnell said: "We campaigned for Remain but many of our MPs, including myself, now represent seats which voted heavily Leave".
Meanwhile, the founder of the Leave.EU Brexit campaign and his chief spin doctor will face further questions from MPs after a fiery clash with a committee investigating "fake news".
The government must start talks with a group of pro-EU Conservative lawmakers to find a new wording for its position on giving parliament a "meaningful vote" on a Brexit deal.