The government fears a weakened negotiating position.
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 in a last-ditch concession by the Government to swerve a revolt, the PM is indicating that it will put forward two of the three parts of Mr Grieve's amendment when the bill returns to the House of Lords.
Addressing Conservative backbenchers in Westminster on Monday evening, the Prime Minister warned if a series of Lords amendments to the EU Withdrawal Bill are approved by MPs, it will send the wrong message to Brussels.
If agreed, ministers would have until the end of November this year to secure a Brexit deal before seeking the approval of parliament.
He confirmed that ministers will seek to overturn 14 amendments which he said would undermine the goal of the Bill and fail to respect the result of the 2016 referendum.
Justice minister Phillip Lee is the first minister to resign over the government's Brexit policy.
The British government was rocked by a resignation and faced anger in Parliament over its Brexit plans, but staved off defeat by offering concessions to MPs who want to soften the terms of the UK's exit from the European Union.
Britain's Secretary of State for Departing the EU David Davis leaves 10 Downing Street in London, June 7, 2018.
"We have listened wherever possible to sensible suggestions that have been made to improve the bill", he said.
"Thirdly, we must under all circumstances respect the result of the referendum".
It is thought that both the government and the Remainer group of Tory MPs consider the outcome to be a success.
Details of the government's commitment will have to be formalised next week in a new amendment to the bill. Grieve suggested that would not be enough to prevent a rebellion. During the debate, potential rebels, including former Attorney General Dominic Grieve were invited out of the chamber for discussions with the Chief Whip Julian Smith.
Earlier, most of the original 11 rebels on the meaningful vote amendment had indicated that they would stand firm.
Dismissing the Government's compromise, she tweeted: "Merely issuing a statement in response would make it a meaningless final vote".
But the former Chancellor Kenneth Clarke has urged pro-EU rebels to hold their nerve, arguing that if they succeeded they would strengthen Mrs May's hand against the Brexit hardliners in the Cabinet. However, it is understood that she had concerns over the Lords amendment on the table.
The major last-minute concession by ministers means the government avoids defeat by 324 to 298.