This change sought to give greater powers to the "sifting committee", which would be established to decide whether recommendations proposed by ministers to amend retained European Union law after Brexit would require a Commons vote.
He proposed an alternate agreement that would give ministers seven days to come up with new terms if Parliament chose to veto the final Brexit deal, and give the government until November 30 to reach a new deal. The government fears a weakened negotiating position.
Brexit campaigners still voiced concern that the concession may open the door to the European Union trying to force Britain into retaining the closest possible ties with the bloc by weakening the government's hand in the talks. Several pro-EU Conservative MPs said they would join the opposition in voting against the government.
Lawmakers backed a government plan, ending a rebellion that would have challenged May's authority at a time when she is increasingly under pressure to move ahead with all-but stalled Brexit talks in Brussels by offering a more detailed plan. It also hit a two-day high versus the euro of 87.78 pence.
"The Brexit secretary has set out three tests that any new amendment has to meet - not undermining the negotiations, not changing the constitutional role of parliament and government in negotiating worldwide treaties, and respecting the referendum result".
MPs in the House of Commons will vote on a raft of amendments produced by the House of Lords, including one at around 3 p.m. GMT (8.30 p.m. IST) that would give parliament an effective veto over Brexit.
Moments later, MPs voted by 324 to 298 to reject a House of Lords amendment to the EU Withdrawal Bill which would have given Parliament the power to tell the PM to go back and renegotiate the Brexit deal she secures from Brussels.
Dismissing the Government's compromise, she tweeted: "Merely issuing a statement in response would make it a meaningless final vote".
His competing amendment could force ministers to hand over control of its Brexit strategy to parliament if there is no deal by mid-February.
Davis on Tuesday told the BBC, "that was the decision of the British people. and whatever we do, we're not going to reverse that".
Britain's Prime Minister Theresa May leaves 10 Downing Street in London, Britain, June 12, 2018.
"The government can not demonstrate the flexibility necessary for a successful deal if its hands are tied midway through that process", he said.
"This needs to be resolved", Andrew Bridgen, a pro-Brexit Conservative lawmaker, told Reuters.
The concession means MPs could be given power to prevent Britain leaving the European Union without a deal.
The problem for the prime minister is that she can't keep both sides happy. One says: "If we do not get what we were promised the Government will be defeated after we have amended the Bill in the Lords".
There is little May can do.
Ms. May's minority government relies on the support of Northern Ireland's Democratic Unionist Party for a slender working majority in the 650-member Commons.
This came after a last-minute resignation by the justice minister Dr Phillip Lee, who said he could no longer look his children in the eye and vote to support the government.
Jeremy Corbyn made fun of the deep divisions within Theresa May's cabinet over Brexit during PMQs on Wednesday, after the prime minister narrowly avoided a humiliating defeat in parliament.