He said Mrs May "has gone back on her word and offered an amendment that takes the meaning out of the meaningful vote".
"This ensures that in all circumstances parliament can hold government to account, while also allowing government to deliver on the will of the British people as expressed in the referendum", a Brexit department spokesman said.
Calm down, says Dominic Grieve, leader of the Tory revolt, in the Evening Standard.
Asked if voting against the Government could bring it down, Mr Grieve told BBC1's Sunday Politics: "We could collapse the Government".
"If the government can't get the most important treaty through Parliament we'll be looking for a new government", said Foreign Affairs Committee chairman Mr Tugendhat.
Now Conservative peer Viscount Hailsham has re-tabled Mr Grieve's amendment in the House of Lords, setting the scene for a fresh Government defeat when the Bill returns to the Second Chamber on Monday.
He said: "I think it is unacceptable because it seems to me to be contrary to what the whole intention was behind this whole amendment".
Despite the "personal assurance" about a new compromise amendment, possibly as early as next week, the government has now indicated that any changes may not go as far as the rebels wanted, says Jessica Elgot in The Guardian.
After a last-gasp meeting with the Prime Minister before a crunch vote on Brexit on Tuesday, up to 17 Tory MPs agreed not to back a plan that could have seen Parliament take control of the Brexit negotiations if the Government failed to strike a deal.
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"The Prime Minister should be left in no doubt; any attempt to water down her promise to give Parliament a "meaningful vote" will end with MPs forcing a defeat on her".
"It all changed without Dominic Grieve or anyone else being consulted".
Sarah Wollaston tweeted: "So just to be clear we are now going to have to amend the "unamendable" after the agreed amendable amendment acquired a sneaky sting in the tail".
Before the vote on the Labour amendment, which the party lost by 322 to 240, lawmaker Laura Smith resigned from her junior role in the team "shadowing" the cabinet office and four others left their roles as parliamentary private secretaries.
The government agreed to discuss elements of a rebel plan to create new checks and balances on the Brexit deal, and where possible incorporate them into the laws that will formally end Britain's European Union membership.
"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".
In the final text of the amendment published on Thursday, no effective veto on a no-deal Brexit is offered to MPs.
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.
Brexit minister David Davis had earlier warned lawmakers that the government would never allow them to "reverse Brexit" or undermine negotiations.