In an appeal for unity, 41 days before Britain's scheduled departure, May said: "History will judge us all for the parts we have played in this process".
Brexit minister Stephen Barclay met Michael Barnier for talks on Monday at the European commission. "And they do know what we want".
Mei plans to find a solution to the border problem.
A flag depicting the British union design and the EU design is seen outside of the Houses of Parliament in London, Britain.
Conservative eurosceptics abstained from Thursday's vote on May's plan to seek last-minute changes to the withdrawal agreement, condemning her minority government to defeat.
Japanese firms, collectively employing around 140,000 people in the United Kingdom, have repeatedly made clear they are anxious at the prospect of a "no-deal" Brexit - for instance, Nissan recently said such uncertainty contributed to its decision to abandon plans to build a new model of one of its flagship vehicles at its Sunderland plant.
Tomorrow, Britain's Attorney General, Geoffrey Cox, is expected to give a speech setting out the changes which would be necessary to make any alterations to the backstop legally acceptable.
Matt Kuchar apologizes and will pay caddie $50,000
He now leads the season-long points race, having also won the Sony Open in January with his normal caddie, John Wood, on the bag. Weighing in on the controversy, six-times major victor Nick Faldo said Kuchar should have been more generous from the outset.
Youth-led climate protests sweep across Europe
Labour leader Jeremy Corbyn, saw it differently, saying it was "inspiring to see them making their voice heard". Scotland Yard said two arrests were made in London.
Klopp fears Bayern Munich are ‘more unsafe than before’
Liverpool will be hoping he turns up with his A-game tonight, because if he does Bayern Munich could be in for a long night. Klopp went on to win two Bundesliga titles with Dortmund before heading to Anfield in October 2015.
In a letter to her MPs, Mrs May pleaded with them to unite and deliver on Brexit.
The Premier said the result was "disappointing" by another Commons defeat on Valentine's Day but vowed that the Government would continue its work to secure changes to the Irish border backstop. But we stand now at a crucial moment.
In a letter to her divided Conservative lawmakers, May asked them to put aside "personal preferences" and unite in the interests of the country by backing a deal.
He continued: 'I don't think it's the mechanism that matters, it's the objective: if you can get to a place where the potential longevity of the backstop, the potential that the backstop lasts forever can be adequately dealt with, that's what we're all seeking to do.
At home, Mr Corbyn is facing concerns that the Labour Party could split over Brexit, with some MPs increasingly frustrated at his failure to back a second referendum on the issue.
She added: "The one problem with last night's vote is that it allows the European Union to continue with this pretence that they don't know what we want".