Boris Johnson has said he will press on "undaunted" with Brexit on 31 October, despite losing a crunch Commons vote.
The PM must now ask the EU for an extension to that deadline after MPs backed an amendment aimed at ruling out a no-deal Brexit, by 322 votes to 306.
Mr Johnson has told EU Council President Donald Tusk that he will now send a letter seeking the delay.
Under the terms of the so-called Benn Act, passed last month by MPs, he has until 2300 BST on Saturday to send it.
Having spoken to Mr Johnson at 1915 BST, EU Council President Donald Tusk tweeted that he was "waiting for the letter".
Waiting for the letter.— Donald Tusk (@eucopresident) October 19, 2019
I just talked to PM @BorisJohnson about the situation after the vote in the House of Commons.
An EU source said that once Mr Tusk received the letter, he would start consulting EU leaders on how to react - which may take a few days, BBC Brussels reporter Adam Fleming reported.
Mr Johnson has vowed to bring in legislation on Monday to implement the deal he struck with Brussels this week.
MPs could also be given another vote on the deal then, if Commons Speaker John Bercow allows it.
The Commons defeat is a major setback for the PM, who has repeatedly insisted that the UK will leave at the end of the month come what may.
Mr Johnson told the Commons he was not "daunted or dismayed" by the defeat and remained committed to taking Britain out by the end of the month on the basis of his "excellent deal".
In a letter to MPs and peers on Saturday evening, he warned the EU could reject "Parliament's request for further delay".
He wrote: "It is quite possible that our friends in the European Union will reject Parliament's request for further delay (or not take a decision quickly)."
He added that it was to his "great regret" that MPs had voted for more delay, and that he "will not negotiate a delay".
"I will tell the EU what I have told the British public for my 88 days as prime minister: further delay is not a solution," he said.
But Labour leader Jeremy Corbyn said: "The prime minister must now comply with the law. He can no longer use the threat of a no-deal crash out to blackmail members to support his sell-out deal."
And the SNP's leader at Westminster, Ian Blackford, said that if Mr Johnson acted as if he was "above the law", he would find himself in court.
Downing Street refused to offer any explanation as to why the prime minister did not consider he was obliged to negotiate a fresh extension.
The EU said it was up to the UK to "inform it of the next steps".
French President Emmanuel Macron spoke to Mr Johnson by phone after his Commons defeat, telling him a delay to Brexit "would be in no one's interest," according to a French official.
MPs had been geared up for a make-or-break vote on Mr Johnson's Brexit deal on the first Saturday sitting of Parliament since the Falklands War 37 years ago.
But in the end there was no vote on whether to back the deal or not.
MPs voted for an amendment tabled by former Conservative MP Sir Oliver Letwin, withholding approval of the deal until the legislation to implement it is in place.
Ministers argue that this would delay Brexit - but Sir Oliver and his supporters, who back the deal, say it is an insurance policy to prevent it turning into a no-deal exit.
The main government motion, as amended, was passed without a vote, meaning the Benn Act kicks in and the prime minister must request a three-month extension.
A second government motion, on a no-deal Brexit, was pulled, meaning an amendment on a second referendum did not go to a vote either.
The voting took place as thousands of anti-Brexit demonstrators marched on Westminster.
Many People's Vote supporters cheered when they learned of Mr Johnson's defeat, and the crowds were later addressed by prominent Remain-supporting MPs including Dominic Grieve and Hilary Benn.
Footage posted to social media showed Conservative ministers Jacob Rees-Mogg and Andrea Leadsom being heckled by People's Vote demonstrators as they left Parliament under police escort.
The EU is not going to rush to take any action following this vote.
As far as it is concerned, it has negotiated a new Brexit deal as requested by the UK government and now it is up to that government to sell that deal.
There is zero appetite in the EU to renegotiate the deal and, if the EU receives a request for a new Brexit extension, don't expect a rush on the EU's side to grant it.
In order to approve or discuss a new extension all EU leaders would have to come back to Brussels, which they left less than 24 hours ago.
The EU Commission now waits to hear from Boris Johnson about what has changed because he promised them at the summit just 24 hours ago that the new Brexit deal would be voted on in Parliament, and approved by the majority of MPs.
If push comes to shove, I cannot see EU leaders saying no to another request for an extension if the alternative would be a no-deal Brexit, which they have wanted so much to avoid.
But that is now all to unfold in the days to come.
Sir Oliver Letwin said Saturday's Commons vote meant the UK would not "crash out" of the EU on 31 October without a deal if the necessary legislation was held up or derailed.
He insisted his aim was not to stop the UK leaving and he would vote for the enabling legislation when it comes forward.
His motion was supported by 10 former Tory MPs who have either quit or been forced out of the party over Brexit, including Philip Hammond, David Gauke and Amber Rudd.
However, six Labour MPs voted against the amendment, as did five former Labour MPs who now sit as independents, which the BBC's Laura Kuenssberg said would give the PM hope of passing his agreement the next time around.
The Democratic Unionists, who backed the Letwin amendment, said the delay would allow for further scrutiny of the PM's agreement - emphasising that its support would depend on preserving the "constitutional and economic" integrity of the UK.
But Brexiteers reacted with anger, Tory MP Peter Bone saying it had been "a complete waste of time".
And the European Commission spokeswoman said it noted the vote.
🇪🇺🇬🇧 @EU_Commission takes note of the vote in the House of Commons today on the so-called #Letwin Amendment meaning that the #WithdrawalAgreement itself was not put to vote today. It will be for the UK government to inform us about the next steps as soon as possible.— Mina Andreeva (@Mina_Andreeva) October 19, 2019
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