Earlier Phillip Lee - who quit as a justice minister to oppose the government on Brexit - received a round of applause after he set out his stance.
Opening debate on the flagship EU Withdrawal Bill in the House of Commons, Mr Davis warned that the "cumulative effect" of a series of Lords amendments would "make it impossible to deliver the smooth and orderly exit we want".
"The main reason for my taking this decision now is the Brexit process and the government's wish to limit parliament's role in contributing to the final outcome in a vote that takes place today", he said in a statement released on his website.
A paper laying out the U.K. government position, due to be published this month, has been delayed because the Cabinet can not agree on a united stance.
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Trump and Kim are expected to meet in Singapore on Tuesday with talks focusing on the denuclearization of the Korean Peninsula. Trudeau has his closing press conference this afternoon.
She insisted: "We must think about the message Parliament will send to the European Union this week".
Crucial to it all will be the 10 DUP votes and they are expected to vote with the Government.
"Whatever we do, we're not going to reverse that", he said.
"I am trying to negotiate the best deal for Britain". If and when agreement can be reached, the new amendment will be introduced in the House of Lords, when the bill returns there in the next stage of its passage through parliament.
A vote on Tuesday on the Lords amendment to give Parliament a meaningful vote on exit arrangements is also looking close for the government. But a government official said they had just agreed to open talks on the basis of the rebel amendment.
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It showed a seemingly glowering German Chancellor Angela Merkel and several other leaders appearing to confront a seated Trump. He also attacked Trudeau's character, calling the Liberal Party leader meek, weak and dishonest.
He offered to use the proposal as the basis of discussions "in good faith" before the bill returned to the Lords, in exchange for support for the government on Tuesday.
The Daily Express, another pro-Brexit tabloid, issued a thinly-veiled threat to lawmakers, saying they should "Ignore the will of the people at [their] peril".
'The goal of the EU Withdrawal Bill is simple - it is putting EU legislation into law to ensure a smooth and orderly transition as we leave, ' she is expected to tell them.
Appearing before the 1922 Committee of backbench MPs, Mrs May argued that the party had to stay united to strengthen her negotiating position in Brussels. "The end of March 2019, we leave the E.U. Full stop".
Labour's Shadow Brexit Secretary Keir Starmer believes that a Norway-style deal with the EU would not prevent a hard border in Northern Ireland and that becoming a member of the European Economic Area (EEA) - effectively keeping Britain in the EU single market - would be "totally incompatible" with the need to avoid a hard border with the Republic of Ireland, the Independent wrote.
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At the summit, Trump refused to endorse a group deal, saying other members use unfair trade practices against the United States. She added that Berlin would continue its dialogue with the United States despite difficulties.