Boris Johnson has sent a request to the EU for a delay to Brexit - but without his signature.
The request was accompanied by a second letter, signed by Mr Johnson, which says he believes that a delay would be a mistake.
The PM was required by law to ask the EU for an extension to the 31 October deadline after losing a Commons vote.
EU Council President Donald Tusk tweeted that he had received the extension request.
He did not provide details of its content, but added that he will now consult EU leaders "on how to react".
Hours after losing a crunch vote in a historic Saturday session in the House of Commons, the prime minister ordered a senior diplomat to send an unsigned photocopy of the call by MPs set out in the so-called Benn Act, passed last month.
A senior Downing Street source said that the hard copy and email copy of the letter would be conveyed by Sir Tim Barrow, the UK's representative in Brussels.
The two letters are also accompanied by a cover note from Sir Tim, explaining that the first letter complies with the law as agreed by Parliament.
The second letter from Mr Johnson - signed off this time - makes clear that he personally believes that a delay would be a mistake.
It appeals to EU leaders to ask MPs to reconsider their decision, and vote for the deal the UK and EU have agreed without any further delays.
The prime minister has previously said he would "rather be dead in a ditch" than ask the EU to delay Brexit beyond 31 October.
BBC Political Editor Laura Kuenssberg described the decision to send three documents as "controversial", predicting "there will be a fight about whether Boris Johnson is trying to circumvent the court".
She added: "This is heading straight for the court, and it may very quickly end up in the Supreme Court."
Earlier, Mr Johnson rang European leaders, including Mr Tusk, to insist that the letter "is Parliament's letter, not my letter".
MPs could also be given another vote on the deal on Monday, if Commons Speaker John Bercow allows it.
The Commons defeat is a major setback for Mr Johnson, who has repeatedly insisted that the UK will leave at the end of the month come what may.
Under the terms of the so-called Benn Act, passed last month by MPs determined to prevent a no-deal Brexit, he has until midnight to send a letter to the EU requesting an extension.
Mr Johnson said he was not "daunted or dismayed" by the Commons defeat and remained committed to taking Britain out by the end of the month on the basis of his "excellent deal".
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".
First Saturday sitting in 37 years
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.
Frustration in Brussels
Frustration has mounted among other EU leaders over the distraction of a process that has dragged on for three-and-a-half years since Britons voted in a referendum to leave the EU.
French President Emmanuel Macron has been the most outspoken and hawkish among the 27's leaders on the issue.
His camp stresses the cost of protracted uncertainty in terms of sapping the EU's political capital and attention to face challenges from climate and migration to international crises, as well as the economic cost for companies that have invested in contingency preparations for a no-deal Brexit.
Despite French misgivings, the EU has made repeatedly clear it would not want to be seen pushing a member state out and that its absolute priority is to avoid a no-deal Brexit, especially one for which it would take the blame if it refused an extension.
However, an extension can only be granted by unanimity among the 27 and, asked whether there was any serious risk that Mr Macron could refuse it, an EU official said: "No."
"If there is a chance of a deal, they will never choose no deal," said Nick Petre, spokesman for the Renew Europe group of liberals in the European Parliament that includes Mr Macron.
It is, however, possible that the EU 27 will grant a "technical extension" of one month - instead of the 31 January deadline Mr Johnson is obliged to request - to give Britain and the European Parliament time to approve the deal clinched this week.
"It can still just be a technical extension, only until the end of November. And they could still get out of it if they manage to pass it before October 31," said an EU diplomat who deals with Brexit.
Many in Brussels believe there could be no more extensions beyond mid-2020 as the bloc needs the rest of the year to prepare its new, long-term budget from 2021 and needs to know whether Britain will go on paying.