Talks between Labour and the government aimed at breaking the Brexit impasse have ended without an agreement.
Jeremy Corbyn said the discussions had "gone as far as they can", blaming what he called the government's "increasing weakness and instability".
Theresa May said the lack of a "common position" within Labour over a further referendum had made talks "difficult".
The prime minister said she would now consider putting options to MPs on Brexit that may "command a majority".
But Irish Prime Minister Leo Varadkar called the end of the talks a "very negative development".
Mrs May has promised to set a timetable for leaving Downing Street following a House of Commons vote on her EU Withdrawal Agreement Bill in the week beginning 3 June.
Brexit had been due to take place on 29 March - but after MPs voted down the deal Mrs May had negotiated with the bloc three times, the EU gave the UK an extension until 31 October.
This prompted negotiations between the Conservatives and Labour to see if the parties could come to a Brexit agreement, despite differences over issues including membership of a customs union and a further referendum.
Why the PM's plan may not be dead yet
The forthcoming leadership contest may firm up opposition to Theresa May's bill on the Conservative benches
By putting the Withdrawal Agreement Bill out of its misery almost as soon as it appears, the prime minister's critics know she will vacate office sooner rather than later.
But some candidates will be keener for her to get Brexit over the line, even with a less than optimal deal, so they don't immediately get bogged down with difficult votes. It would also allow them to make their pitch based on the future relationship with the EU.
So could some of their supporters - irrespective of their public criticism of the deal - quietly vote to get it over the line?
But in a letter to the prime minister, Labour leader Mr Corbyn wrote: "I believe the talks between us about finding a compromise agreement on leaving the European Union have now gone as far as they can."
The move towards choosing her replacement meant "the position of the government has become ever more unstable".
He later said his party had negotiated "in good faith and very seriously, and put forward a lot of very detailed arguments", which he thought was "the responsible thing to do".
He added: "The issue [is] that the government has not fundamentally shifted its view and the divisions in the Conservative Party mean the government is negotiating with no authority and no ability that I can see to actually deliver anything."
Speaking after meeting Tory activists in Bristol, Mrs May said: "There have been areas where we have been able to find common ground, but other issues have proved to be more difficult.
"In particular, we haven't been able to overcome the fact that there isn't a common position in Labour about whether they want to deliver Brexit or hold a second referendum to reverse it."
She said the government would consider what had come out of the meetings with Labour and "consider whether we have some votes to see if the ideas that have come through command a majority in the House of Commons".
Labour's favoured plan includes a permanent customs union with the EU, meaning no internal tariffs (taxes) on goods sold between the UK and the rest of the bloc.
It also keeps the option of a further referendum on the table, giving the public a say on the deal agreed by Parliament.
Both scenarios have caused anger among Brexit-backing Conservatives, who claim a customs union would prevent the UK from negotiating its own trade deals around the world after leaving the EU, and who believe another public vote is undemocratic.
Some MPs have also criticised Mrs May for even entering into talks with Labour, but the prime minister said the government had "no choice but to reach out across the House of Commons".
Before the talks with Labour, the prime minister - whose Conservative Party does not have a majority in the Commons - failed to get her deal through three times, by margins of 230, 149 and 58 votes.
The DUP, which supports her government on certain issues, opposes Mrs May's agreement with the EU over its implications for Northern Ireland.
Following the collapse of the discussions with Labour, DUP leader Arlene Foster said: "This round of talks has wasted time rather than making progress and reducing uncertainty. It was always doomed to failure."
Shadow Brexit secretary Sir Keir Starmer said the PM was "trying to blame everyone but herself for the collapse of cross-party talks".
He tweeted: "She knows the reality is she couldn't carry her own side or offer a realistic compromise. Any deal agreed wouldn't last a day under a new Tory leader."
But Brexit Secretary Stephen Barclay said the government had moved in some areas - specifically on workers' rights and environmental standards - and had been "having discussions around where we were on customs arrangements".
He said senior Labour figures like Sir Keir had been insisting on a further referendum on any deal, adding: "It begs the question why have they taken six [or] seven weeks for talks?"
Liberal Democrat leader Vince Cable criticised both of the main parties, tweeting: "The weakness of the government and the vacillation of the Labour Party put their talks on very shaky ground from the beginning."
The director general of the CBI business group, Carolyn Fairbairn, called the end of the talks "another day of failed politics" and "another dispiriting day".
She called for Parliament's recess at the end of this month to be cancelled, adding: "This is no time for holidays. It's time to get on with it."
On Thursday, former Foreign Secretary Boris Johnson became the latest MP to put his name forward as a possible successor to Mrs May.
Asked by reporters on Friday if he would be running for the leadership, Environment Secretary Michael Gove said it was now time for colleagues to "focus" on delivering Brexit.