He called for Brexit to be delayed, and for the public to get a second referendum on the terms of any exit deal.
"I have agreed this morning with the Brexit Secretary that we will bring forward an amendment in the Lords".
The pro-independence party accuses the British government of trying to seize powers that will be handed back from Brussels after Brexit and which the SNP believes should go to Scotland's Edinburgh-based parliament. Ministers originally wanted to make this a vote to either accept the deal or to leave without a deal.
Anti-Brexit Labour MP Chuka Umunna described the "climb-down on giving Parliament a meaningful vote" as "significant".
The British public might have narrowly voted for Brexit, but what that Brexit looks like-from customs and immigration to the timing of the final exit-depends on the deal now being hashed out with the European Union.
Before the vote, she assured lawmakers she would honour her promise and deal with the "concerns raised about the role of parliament in relation to the Brexit process".
The upshot of the shift may well be as dramatic as the parliamentary procedure is incomprehensible.
However, although the prime minister was spared the complication and embarrassment of defeats of Wednesday, issues like customs are set to be revisited in a few weeks time when more Brexit-related legislation is put to MPs.
"But this remains hypothetical and the Government is confident we will agree a good deal with the European Union which Parliament will support", it added in a statement.
"The Labour Party respects the outcome of the European Union referendum and does not support the EEA or "Norway model" as it is not the right for option for Britain". Having passed through its commons stages relatively unscathed it saw a series of 15 government defeats in the House of Lords, including an unexpected one on the single market.
Downing Street said it would publish a compromise amendment on Thursday, which will go to the Lords for debate on Monday, and then back to MPs later next week.
But Brexit campaigners feared it could weaken Britain's negotiating stance in talks to leave the European Union and the Brexit ministry was quick to put out a statement saying: "We have not, and will not, agree to the House of Commons binding the government's hands in the negotiation".
Brexiteers were dejected by the turn of events, but are pinning their immediate hopes on the detail in the government's compromise.
Another Conservative Remainer, former Cabinet minister Nicky Morgan, denied that the rebels had been "played" by the Prime Minister.
While Conservatives at Westminster say some of these must come to Parliament to allow for common frameworks to be established in areas such as agriculture and environmental regulations, ministers at Holyrood fear the powers of the Scottish Parliament could be restrained for up to seven years. He said he would vote against the prime minister.
The Labour MP claimed she "was not in that team" and backed "Keir Starmer and his amendment and trust they can deliver". She said her committee had heard evidence about the measures other European Union member states were applying to introduce some control over migration, which she had been told could be a way of the United Kingdom having full single market access without free movement. We'll have to wait and see.