Theresa May will allow Conservative MPs to back a Labour call for Parliament to "properly scrutinise" the Government's Brexit strategy.
The move is seen as an attempt by the prime minister to see off a backbench rebellion and appease Tories who are said to be increasingly unhappy at being denied the chance to vote on the plan.
A Labour source had said there was a "very real possibility" that rebellious Tories could back the party's motion in a Commons debate today, which calls for MPs to be given proper scrutiny before Article 50 of the EU treaties is triggered.
But Mrs May has now tabled an amendment which will allow Tories to back the text of Labour's motion but adds caveats insisting that the EU referendum result must be respected and that the Government's negotiating strategy should not be undermined.
A Labour source described it as "one hell of a climbdown" and said the party had been sounding out Tory MPs who are "very unhappy" with the situation.
"They're clearly trying to do everything they can do to avoid a vote but given their position was they didn't think Parliament should have any role that's one hell of a climbdown," the source said.
Labour's motion, which would not bind the Government to act on it if approved, reads: "That this House recognises that leaving the EU is the defining issue facing the UK; believes that there should be a full and transparent debate on the Government's plan for leaving the EU; and calls on the Prime Minister to ensure that this House is able properly to scrutinise that plan for leaving the EU before Article 50 is invoked."
Mrs May's amendment, tabled on Tuesday night, adds to Labour's motion "and believes that the process should be undertaken in such a way that respects the decision of the people of the UK when they voted to leave the EU on 23 June and does not undermine the negotiating position of the Government as negotiations are entered into which will take place after Article 50 has been triggered".
The effect of the amendment will mean that Tory MPs can vote with the Government while simultaneously backing Labour's call without voting for the Opposition motion on its own, if a division is called on Wednesday.
A No 10 source insisted the Prime Minister's position on parliamentary scrutiny of Brexit has not changed.
"The Government is focused on delivering on Brexit," the source said."We have always been clear that while we should do nothing to undermine our negotiating position, Parliament has an important role to play, and this motion reflects that."
Mrs May has said she intends to triggers Article 50 before the end of next March.