Another failure means MPs will hold more votes to try to agree a way forward, as the PM hints at the prospect of an election.
Theresa May is considering a last-ditch attempt to save her Brexit deal after suffering a third defeat in the Commons.
The prime minister is weighing her next moves after her deal was voted down by 286 votes to 344.
She said the implications of the vote were "grave", adding: "I fear we are reaching the limits of this process in this House".
The Prime Minister has been urged by some in her own cabinet to embrace a no-deal Brexit.
Sky News political editor Faisal Islam said a delegation of ministers went to Downing Street after the vote to urge the PM to reject a softer Brexit and go for no deal.
Downing Street sources have suggested the prime minister has not given up hope of getting it through the Commons, pointing out that the scale of the defeat was significantly smaller than in the previous two votes.
On the day that Britain was meant to have left the EU, thousands also gathered in Westminster to demand MPs deliver the result of the 2016 referendum.
Boris Johnson, Jacob Rees-Mogg and Dominic Raab switched sides at the last minute and voted for the agreement after the PM said she would quit if the deal passed.
But 34 Tories still rebelled, and Northern Ireland's DUP stood firm against it because of concerns about the Irish border backstop.
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Labour also opposed the agreement, with only five of the party's MPs voting in favour.
The government must now present a new way forward to the EU by 12 April or face leaving the EU without a deal on that date.
MPs will consider further options through a series of indicative votes in parliament next week.
Options include remaining in a customs union, holding a second referendum, or no deal.
The EU has called an emergency summit on 10 April to discuss the implications of the vote.
Mrs May said Friday's vote means Britons will "almost certainly" have to elect MEPs to the European Parliament in elections taking place at the end of May.
After the vote, the PM's official spokesman refused to deny four times that she is now considering a general election.
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Labour leader Jeremy Corbyn said he backed that idea and called for Mrs May to quit.
"The House has been clear this deal now has to change. There has to be an alternative found," he said.
"If the prime minister can't accept that then she must go. Not at an indeterminate date in the future, but now, so that we can decide the future of this country through a general election."
Nigel Dodds, the DUP's Westminster leader, told Sky News that Mrs May had "brought about this situation almost entirely single-handedly".
"Back in December 2017 she agreed to this idea of a backstop and as we now know the European Union was staggered that they ever agreed to it.
"This has been like a noose around the neck of the negotiations ever since."
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Liberal Democrat leader Sir Vince Cable said he believed the only way the European Union would give the UK another Brexit extension - to avoid a no-deal exit - would be if there was a general election or another referendum.
"I think a referendum is much the best way of resolving this now," said Sir Vince.
Even though Britain's Brexit day failed to materialise, Leave parties were held in central London.
Arriving at one party, Nigel Farage, former UKIP leader who spearheaded Brexit, was asked what he would like to see: "Brexit", he replied.
Five people were also arrested as thousands attended the pro-Brexit March to Leave.
The final leg of the march, which began in Sunderland two weeks ago, saw protesters walk from Fulham towards Parliament Square.
Mr Farage joined the march and it featured speeches from English Defence League founder Tommy Robinson and UKIP leader Gerard Batten.
Police said two people were held on suspicion of assault, one for being drunk and disorderly and another for assaulting a police officer.
A fifth person was arrested after being wanted for an offence in Hertfordshire.
More demonstrations are lined up for Saturday.
Pro-Brexit "yellow vest" protesters will descend on Whitehall in central London, while a smaller number of anti-Brexit demonstrators are expected to gather at six locations on the Northern Ireland border.
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