Speaking in the House of Commons before MPs began debating amendments to a Bill authorising her to start formal Brexit negotiations, the prime minister urged MPs to reject an amendment calling for a unilateral guarantee.
Labour claimed the move as a "significant victory" in response to its repeated demands for a "meaningful" vote at the end of the two-year negotiation process.
The amendment on European Union citizens' rights and another calling for parliament to have a vote on the final Brexit deal are the only proposed amendments likely to attract cross-party support. This directly contradicts Jeremy Corbyn's repeated assurances that Labour would reserve the right to oppose this bill at third reading if its amendments to include vital safeguards for Parliament and the British people were not accepted.
The prime minister wants lawmakers to pass the bill quickly so she can meet her deadline of triggering Article 50 by March 31.
"The message is clear to all: This House has spoken and now is not the time to obstruct the democratically expressed wishes of the British people", she said on Monday.
Rebels from the Conservative Party have threatened to vote with Labour and the SNP on changes to the EU (Notification Of Withdrawal) Bill.
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"The vote they're offering - which will give MPs a choice between an extreme Brexit and falling off a cliff edge into WTO trade rules - isn't a concession, it's an ultimatum".
"A good deal may be possible, and it is in all our interests to ensure this is the case, but we could be about to commit this country to a path which will leave us weakened and damaged".
Shadow Brexit secretary Keir Starmer said this was a "huge and very important concession" by the government.
The party leader's imposition of a three-line whip - the toughest sanction available - means any shadow minister wanting to rebel could have to resign.
If lawmakers chose to reject the deal, the United Kingdom would have no trading agreement with the European Union and would have to revert to World Trade Organization terms, Clarke said. While they are unlikely to give the Bill an easy passage, they are expected to give way eventually to the elected house, avoiding a constitutional crisis.