British Prime Minister Theresa May will ask the EU for an extension to the Brexit deadline to "break the logjam" in Parliament.
The PM says she wants to meet Labour leader Jeremy Corbyn to agree a plan on the future relationship with the EU.
But she insisted her withdrawal agreement - which was voted down last week - would remain part of the deal, the BBC reports.
Mr Corbyn said he was "very happy" to meet Mrs May, and would ensure plans for a customs union and protection of workers' rights were on the table.
The cross-party talks offer has angered Tory Brexiteers, with Boris Johnson accusing ministers of "entrusting the final handling of Brexit to Labour".
The former foreign secretary said Brexit was "becoming soft to the point of disintegration" and he could never agree with staying in a customs union.
BBC political editor Laura Kuenssberg said it probably means the prime minister is likely to adopt a closer relationship with the EU - a softer Brexit - than she had agreed so far.
The UK has until 12 April to propose a plan to the EU - which must be accepted by them - or it will leave without a deal.
Mrs May agreed a deal with the EU in November 2018, but it has been voted down twice in Parliament by huge margins, and a separate deal just on the withdrawal agreement section lost by 58 votes on Friday.
MPs have also twice held indicative votes to try to find a consensus, but none of the proposals won a majority.
The UK was supposed to leave the EU on 29 March, but Mrs May agreed a short extension after realising Parliament would not agree a deal by the deadline.
In a statement in Downing Street, Mrs May said she wanted any further extension to be "as short as possible" - before 22 May so the UK does not have to take part in European elections.
She said she wanted to agree a new plan with Mr Corbyn and put it to a vote in the Commons before 10 April - when the EU will hold an emergency summit on Brexit.
If she and Mr Corbyn do not agree a single way forward, she proposed putting a number of options to MPs "to determine which course to pursue".
But the EU would still have to agree to any extension.
The BBC's Europe editor Katya Adler warned their demands "haven't changed at all", and they are preparing "pretty strict conditions" for any further delay.
"Even though Theresa May says she doesn't want to, EU leaders will ask her to prepare the UK to take part in European Parliamentary elections by the end of May because they don't believe she will be able to get her Brexit house in order before then," Adler said.
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