Theresa May believes the UK is in "crisis" over Brexit after she was blocked from bringing an unchanged withdrawal agreement back to the House of Commons, Downing Street has said.
The prime minister and her cabinet discussed Brexit for an hour-and-a-half on Tuesday following a major intervention by House of Commons Speaker John Bercow.
Citing a centuries-old convention on Monday, Mr Bercow blocked Mrs May from bringing back her twice-defeated Brexit deal for a third vote in the Commons unless it is "substantially" different.
Prior to the speaker's ruling, the prime minister had been expected to hold another vote on her withdrawal agreement this week before a summit of EU leaders on Thursday.
She will now write to European Council President Donald Tusk, setting out the UK's position in relation to an extension to the Article 50 period and a delay to Brexit.
Environment Secretary Michael Gove later confirmed Mrs May would set out "today or tomorrow" the terms of her request.
He also told Sky News he believes there will be "another chance for the House of Commons to reflect on where we are", with "progress" coming "in the next few days".
Asked if another vote on Mrs May's Brexit deal could be held this week or next, Mr Gove said: "That's a decision for the prime minister but I think the sooner we can have a vote, the better."
Mrs May has previously said MPs finally approving her Brexit deal this week would see a short delay, but a continuing failure to back a withdrawal agreement would likely mean a much longer extension to the UK's membership of the EU.
The prime minister has also warned this would mean the UK has to take part in EU elections in May.
Mr Bercow's action saw Solicitor General Robert Buckland immediately claim the government was facing a "major constitutional crisis".
Asked after Tuesday's cabinet meeting whether Mrs May agreed, the prime minister's official spokesman highlighted how she had predicted a "moment of crisis" should MPs vote down her deal for a second time, prior to them doing so last week.
The spokesman said: "Events yesterday tell you that situation had come to pass."
He added Mrs May's message to the country is that there is "an absolute determination to find a way that parliament can find a way to leave with a deal".
"She wants that to happen as soon as possible, she does not want a long delay and asking UK to participate in [European Parliament] elections would be a failure."
He said Mrs May believes any extension should be "as short as possible" and does not believe holding a general election would be in the "national interest".
It has been suggested Mrs May could agree a long delay to Brexit with EU leaders this week, but with an exit clause should MPs eventually support a withdrawal agreement.
Last week, five cabinet ministers rebelled against the government to reject a no-deal Brexit in all circumstances.
Sky News understands Leader of the House of Commons Andrea Leadsom told her fellow ministers on Tuesday: "This used to be the cabinet that would deliver Brexit and now from what I'm hearing it's not."
Prior to the cabinet meeting, Brexit Secretary Stephen Barclay admitted that, if the UK is to leave the EU with a divorce deal, this would no longer be on 29 March as Mrs May once promised.
He told Sky News: "I don't want an extension but we are now in a situation where we do need an extension to pass the legislation for the withdrawal bill."
Some Conservative MPs have dismissed the impact of Mr Bercow's ruling on the prime minister's Brexit strategy.
Former Tory minister Nick Boles posted on Twitter: "Not sure what all the fuss is about.
"If the PM thinks she has a majority for a third meaningful vote, she will also have a majority for a motion to set aside the Speaker's ruling on the Erskine May convention."
But, Tory Brexiteer James Gray - who has twice opposed the prime minister's deal but was ready to vote in favour of it this week - told Sky News: "It seems to me very likely, as a result of Mr Bercow's ruling yesterday, there will be a huge extension to Article 50 over the weekend [and] no deal is off the table.
"My suspicion is, this is the end of Brexit. I don't think Britain will leave the EU, I think Mr Bercow's ruling will have that effect."
Mrs May's deputy, Cabinet Office minister David Lidington, was in Brussels for talks with EU figures including European Parliament Brexit coordinator Guy Verhofstadt and Brexit negotiator Michel Barnier.
European Council President Donald Tusk was in Dublin to meet Irish prime minister Leo Varadkar.
Mr Tusk said he used the meeting to "confirm full EU unity on Brexit, discuss latest developments and uncertain political situation in London as well as preparedness for a no-deal Brexit".
Labour leader Jeremy Corbyn has held "constructive" cross-party talks with the leaders of the SNP, Liberal Democrats, Greens and Plaid Cymru in a bid to "find a consensus" on Brexit, as well as a group of MPs pushing for a Norway-style relationship with the EU.
Referencing the cross-party talks, a party spokesperson said they "affirmed their common opposition to the government's botched deal or a no deal outcome", while Mr Corbyn called on them to help find a majority for a deal involving a "close economic relationship with the EU that can work for the whole country".
Green Party co-leader Caroline Lucas said Mr Corbyn "certainly didn't rule out the idea" of supporting a second referendum, but Lib Dem leader Sir Vince Cable said "fundamental differences" exist between the other parties and Labour.
Mr Corbyn said Labour's Brexit alternative is "the basis for discussions" and that a public vote should only be held "after Parliament has made some kind of decision".
Mr Bercow confirmed in the Commons on Tuesday that the PM must put down an amendable Brexit motion by next Monday, regardless of what happens in the next few days, raising the prospect of MPs once again trying to alter the Brexit process by tabling amendments.