Theresa May will make a direct plea to EU leaders later asking to postpone Brexit for three months, hours after telling the British public a delay was "a matter of great personal regret".
At an EU summit in Brussels, she will try to persuade the other 27 countries to delay the UK's exit beyond 29 March.
On Wednesday, the PM made a speech blaming the delay on MPs and telling the nation she was "on their side".
Meanwhile, Jeremy Corbyn is also due in Brussels for separate Brexit talks.
The Labour leader will meet the EU's chief Brexit negotiator, Michel Barnier, and the leaders of seven European countries to discuss alternatives to Mrs May's Brexit plan and to say that he believes a different deal can be struck.
The UK is set to leave the EU next Friday unless the law is changed. The current default position for leaving is without a withdrawal agreement, or divorce deal.
Mrs May agreed a deal with the EU, but MPs have rejected it twice.
She has asked the EU for a short extension of the two-year Brexit process – Article 50 – until 30 June, in the hope that it is enough time for MPs to back her deal. However, any extension needs to be agreed to by all EU members.
European Council President Donald Tusk said he believed the EU would agree to a short extension, but this would only be if Mrs May's deal is signed off by MPs next week. Another EU summit next week could be called in an emergency if needed, he said.
Mr Tusk said the "question remains open" as to how long a delay the other EU leaders would support.
But, in her speech from Number 10 on Wednesday, Mrs May insisted she would not be willing to postpone Brexit any further than 30 June, despite appeals from some MPs for a longer extension to give time for a change in direction.
She added: "Of this I am absolutely sure. You, the public, have had enough.
"You are tired of the infighting, tired of the political games and the arcane procedural rows, tired of MPs talking about nothing else but Brexit when you have real concerns about our children's schools, our National Health Service, knife crime.
"You want this stage of the Brexit process to be over and done with. I agree. I am on your side."
She said it was now up to MPs to decide whether they wanted to leave with her deal, no deal or not to leave at all. But she warned that the latter option could cause "irreparable damage to public trust" in politicians.
By Laura Kuenssberg, BBC political editor
It's not me – it's them.
Theresa May has pitched herself tonight against Parliament and on the side of the people.
It's true that No 10 believes strongly that swathes of the population have simply had enough of Brexit.
The way it drowns out other public concerns, the way its processes, contradictions and clamour have wrapped their way around the normal workings of Westminster – remote at the best of times and downright bizarre at the worst.
But, when it is MPs the prime minister needs to get on side if she is to have a real chance of finally getting her deal through next week – third time extremely lucky – the choice of message was not without risk.
Mrs May's remarks provoked an angry response from MPs across the House of Commons, with some calling her comments "toxic" and "reckless".
Mr Corbyn said she was "in complete denial about the scale of the crisis" facing the country and was "unable to offer the leadership the country needs".
Labour's Lisa Nandy described Mrs May's statement as "disgraceful" for "pitting Parliament against the people", while fellow Labour MP Wes Streeting added it was "incendiary and irresponsible" at a time when some MPs had received death threats.
Pro-EU Tory Sam Gyimah, who quit as a minister over her deal, described her remarks as "toxic" and said the "blame game" was "a low blow".
Conservative MP and Remain supporter Dominic Grieve said her "attack on the integrity of MPs is very unfortunate".
But the government's Communities Secretary James Brokenshire said both the prime minister and the country feel "frustration" at not getting her deal through Parliament.
He told BBC Newsnight: "She has been straight with the public, saying we need to not play games, not see the different subterfuges that we have experienced over last number of weeks, to actually crystallise this, to write this down, and make it real.
"The fact is that we have a duty and a responsibility to give effect to that referendum and actually frame the choices and the consequences as well."
EU leaders are expected to begin arriving at the two-day summit from 13:00 GMT on Thursday.
The BBC's Europe correspondent Kevin Connolly said the EU side "appears to hold all the aces" at the summit. He said some countries such as France have been "sceptical of the value of making an offer" of an extension.
Before the summit begins, Mr Corbyn will meet Mr Barnier, Martin Selmayr, the secretary-general of the EU Commission, two EU commissioners and seven EU prime ministers.
Speaking ahead of the meetings, he said Mrs May's "botched deal" should not be brought back to Parliament for a third vote.
He said: "After serious talks with senior MPs from across parliament, I believe it should be possible to agree a deal with the EU that secures a close economic relationship before the European Parliament elections. I look forward to discussing this with European leaders today."
"We believe that consensus can be based on our alternative plan, which would provide protection for manufacturing and jobs, guarantee our rights and end the chaos and uncertainty that the government is inflicting on our country."
Mrs May met opposition leaders before her speech on Wednesday evening to discuss a Brexit delay, but sources told the BBC that Mr Corbyn walked out and other leaders remained unimpressed with what they heard.