Prime Minister Theresa May has insisted she had to reach out to Labour in a bid to deliver Brexit or risk letting it “slip through our fingers”.
In a statement on Saturday night, Mrs May said there was a “stark choice” of either leaving the European Union with a deal or not leaving at all.
Some Conservatives have criticised her for seeking Labour’s help after MPs rejected her Brexit plan three times.
Three days of talks between the parties ended without agreement on Friday.
Labour leader Jeremy Corbyn said he was “waiting to see the red lines move” and had not “noticed any great change in the government’s position”.
He is coming under pressure from his MPs to demand a referendum on any deal he reaches with the government, with 80 signing a letter saying a public vote should be the “bottom line” in the negotiations.
In the statement, Mrs May said that after doing “everything in my power” to persuade her own party – and their backers in Northern Ireland’s DUP – to approve the deal she agreed with the EU last year, she “had to take a new approach”.
“We have no choice but to reach out across the House of Commons,” the prime minister said.
“The referendum was not fought along party lines and people I speak to on the doorstep tell me they expect their politicians to work together when the national interest demands it.”
Getting a majority of MPs to back a Brexit deal was the only way for the UK to leave the EU, Mrs May said.
“The longer this takes, the greater the risk of the UK never leaving at all.”
The UK is due to leave the EU on 12 April and, as yet, no withdrawal deal has been approved by the House of Commons.
Shadow home secretary Diane Abbott told BBC Radio 4’s Today programme Labour had engaged in talks “in good faith” and wanted them to continue.
However, she said there was concern the government has made “no movement” on her party’s demand for changes to the political declaration – the section of Mrs May’s Brexit deal which outlines the basis for future UK-EU relations.
The document declares mutual ambitions in areas such as trade, regulations, security and fishing rights – but does not legally commit either party.
Downing Street has indicated it was “prepared to pursue changes” in order to secure a deal, and Chancellor Philip Hammond said on Saturday that he was “optimistic” the talks could reach “some form of agreement”.
However, Tory Brexiteers have reacted angrily to the prospect of Mrs May accepting Labour’s demands, particularly for a customs union with the EU which would allow tariff-free trade between members but bar them striking their own trade deals.
Leaving the EU’s customs union was a Conservative manifesto commitment, and former party whip Michael Fabricant predicted “open revolt” among Tories and Leave voters if MPs agreed to it.
Former Brexit minister Steve Baker hit out at efforts to recruit MPs to sign a “toxic” letter endorsing the PM’s cross-party efforts, which he said had party members “recoiling in horror”.
And the Sunday Telegraph reported some activists were refusing to campaign for the party, while donations had “dried up”.
Mrs May has written to European Council President Donald Tusk to request an extension to the Brexit process until 30 June but says if MPs agree a deal, the UK should be able to leave before European parliamentary elections are held on 23 May.
She says the UK would prepare to field candidates in May’s European Parliament elections if MPs failed to back a deal.
But Education Minister Nadhim Zahawi told the Today programme it would be “a suicide note of the Conservative Party if we had to fight the European elections”.
Labour is also split over its Brexit approach.
The letter organised by the Love Socialism Hate Brexit campaign contains the signatures of four shadow ministers and argues that any compromise deal agreed by Parliament will have “no legitimacy if it is not confirmed by the public”.
As the political declaration is not legally binding, and with Mrs May having promised to stand down once a Brexit deal is passed, the letter points out that “any future Tory prime minister could simply rip up” assurances given to Labour over future relations with the EU.
However, a letter signed by 25 Labour MPs on Thursday argued against another public vote.
They warned it would “divide the country further and add uncertainty for business” and could be “exploited by the far-right, damage the trust of many core Labour voters and reduce our chances of winning a general election”.