"The majority of MPs will not support a cliff-edge no-deal Brexit & will insist on a meaningful vote".
Mr Grieve's amendment would have given Parliament the power to dictate the next steps if the Government failed to achieve a Brexit deal by February 2019.
The rebels' proposal will come up against the government proposal in the House of Lords on Monday, and will then be discussed again in the Commons on Wednesday.
"I voted on Tuesday to make sure that the sovereign institution of this nation, our Parliament, gets its full sovereign right to review our new relationship with the trading partners we will have in future".
However, the amendment to the EU Withdrawal Bill tabled on Thursday leaves Parliament facing a "deal or no deal" choice.
Created to address concerns aired by pro-EU Conservative backbenchers, the amendment suggests that Parliament should have a say on the final Brexit deal.
Asked if the prime minister's words ruled out a discussion on the contentious rebel clause, her spokesman said: "I think that is a fair assessment".
Mr Grieve had originally wanted the amendment to say that the government must seek the approval of Parliament for its course of action - and that ministers must be directed by MPs and peers in the House of Lords.
Brexit supporters on the 1922 Committee - made up of Tory MPs who do not hold Government positions - were swift to react once the implications of these concessions became clear, with one senior Leaver remarking: "If Theresa and [Chief Whip Julian Smith] have sold us out here they are in real trouble".
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Conservative MPs are now accusing other members of Mrs May's Government of "hijacking" the process to force the Prime Minister to backtrack at the last minute on a pledge to ensure their concerns were addressed.
Shortly before the text of the amendment was tabled, former minister Anna Soubry tweeted to say that "deal or no deal Parliament will have a meaningful vote and ... there will be no hard Brexit" but after the proposal was published she said "without consultation what was agreed earlier today has been changed".
"It all changed without Dominic Grieve or anyone else being consulted".
Sarah Wollaston, who is also unhappy with the current state of the government's flagship Brexit bill, claimed a compromise agreed with ministers had "acquired a sneaky sting in the tail" by the time it was formally tabled.
Labour's shadow Brexit secretary Sir Keir Starmer told the government their amendment is "simply not good enough".
"But it's also important that Parliament can not and should not overturn the will of the British people, which was to leave the European Union".
Brexit minister David Davis had earlier warned lawmakers that the government would never allow them to "reverse Brexit" or undermine negotiations.
For now, May saw off a revolt that would have challenged her 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.
Mr Tugendhat suggested there was no need to "beef up" the "meaningful vote" which now offers parliament the choice between the government's deal and Britain leaving the European Union with no deal.