"It's not practical, it's not desirable and it's not appropriate", Davis said.
The Government is expected to table a compromise amendment on Thursday to her flagship EU Withdrawal Bill, setting out in more detail the terms of the "meaningful vote" promised to MPs on the final Brexit deal. The strained parliament session underlined deep divisions over Britain's European Union exit.
The House of Lords amended the Bill so that if MPs reject the deal, they can direct ministers to go back and renegotiate.
Hours before the debate began, a justice minister resigned in protest at what he called its "wish to limit" the role of parliament in shaping Brexit.
Former deputy prime minister Damian Green wrote in the Sunday Express that the majority of the crucial votes would "pass easily".
British Prime Minister Theresa May faces a knife-edge vote in parliament on Tuesday on her centerpiece Brexit legislation, despite her last-minute warning that defeat risks undermining her negotiations with Brussels.
May said the government would amend the bill to address legislators' concerns, but warned that "I can not countenance Parliament being able to overturn the will of the British people".
The votes follow another bruising week for Mrs May over Brexit which saw David Davis reportedly threaten to resign unless there were changes to the Government's latest "backstop" proposal to avoid a hard border between Northern Ireland and the Republic if there is no overall deal.
The vote on Tuesday is the first of two days of debate that will test May's authority and her plans for leaving the EU.
Anna Soubry, a pro-EU Conservative lawmaker, said she knew of one legislator who would not vote with their conscience because of "threats to their personal safety" and that of staff and family.
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May's spokesman James Slack said Monday that a promised document setting out the government's negotiating position would not be released before a June 28-29 European Union summit, as previously planned.
On Wednesday, parliament will also consider a challenge to her commitment to leave the EU's single market and customs union, which will transform Britain's future trading relationships for many years to come.The House of Lords defeated the government 15 times in earlier votes, offering parliament the chance to put pressure on May and her government to change tack on Brexit.
A section of Labour MPs are expected to defy the official party position and vote in favor of a Lords amendment to keep the United Kingdom in a Norway-style trading arrangement, better known as the European Economic Area (EEA), post-Brexit.
The former attorney general told Press Association: "The Prime Minister agreed that the amendments we had tabled, and the issue that we had raised about Parliament's role in the event of no deal was an important one, and undertook to work with us to put together amendments to present in the Lords which would address those concerns". But a government official said they had just agreed to open talks on the basis of the rebel amendment.
Eurosceptics urged the government to hold firm, saying the rebels were seeking to undermine the 2016 referendum vote for Brexit.
"And she has given us that, and those discussions on how we are going to build on the amendment that has been approved by the House of Commons will start today".
May had faced the prospect of losing the vote on the customs union after rebels had indicated their support for a change introduced by the House of Lords to require ministers to report what efforts they had made to secure a customs union.
The increasingly febrile atmosphere comes as pressure builds for a deal by October ahead of Britain's withdrawal from the European Union in March next year.
Losing the vote in the Commons would have spelt serious trouble for Mrs May, whose position as prime minister was weakened a year ago when she lost her parliamentary majority after calling a general election.
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