Theresa May is to meet MPs to try to find a way forward for Brexit, after her slim victory in the no-confidence vote.
The PM saw off a bid to remove her government from power by 325 to 306 votes, the day after her plan for leaving the EU was rejected.
Afterwards, Labour leader Jeremy Corbyn refused to join talks unless the threat of a no-deal exit was ruled out.
The PM said she wanted to approach discussions in a “constructive spirit”.
Speaking outside Downing Street after talks on Wednesday night with the Lib Dems, SNP and Plaid Cymru, Mrs May called on MPs to “put self-interest aside”.
She must present a new plan for EU withdrawal to Parliament by 21 January.
“It will not be an easy task, but MPs know they have a duty to act in the national interest, reach a consensus and get this done,” she said.
The prime minister is expected to hold meetings with both Tory Brexiteers and the DUP – both of whom rejected her withdrawal deal earlier this week – on Thursday.
BBC assistant political editor Norman Smith said that Environment Secretary Michael Gove, Cabinet Office Minister David Lidington and Brexit Secretary Steve Barclay will also hold talks with senior opposition politicians.
However, when asked what the government was willing to compromise on, Conservative Party chairman Brandon Lewis refused to give specifics.
He told BBC Radio 4’s Today programme that Mrs. May would not consider a customs union and that he did not believe a new referendum was “the right way to go”.
The UK is due to leave the European Union on 29 March.
Meetings, on their own, are not a Plan B. Conversations, are not by themselves, compromises.
To get any deal done where there are such clashing views all around, it requires give and take. It feels like a political lifetime since there has been a fundamental dispute in the cabinet, in the Tory party and across Parliament. Theresa May has stubbornly, although understandably, tried to plot a middle course.
But that has failed so spectacularly at this stage. Ultimately she may well be left with the same dilemma of which way to tack.
It’s clear, wide open, in public that the cabinet is at odds with each other. Just listen to David Gauke and Liam Fox on whether a customs union could be a compromise for example.
The answer for her is not suddenly going to emerge from a unified tier of her top team. There are perhaps five or six of the cabinet who would be happy to see that kind of relationship as a way to bring Labour on board.
What happened in the vote of no confidence?
The prime minister survived a vote of no confidence in her government by a margin of 19 votes, thanks to the backing of the 10 members of the DUP. Had they switched allegiance, the government would have lost by one vote.
This came after MPs voted against Mrs May’s plans for Brexit on Tuesday night by a historic margin when it was rejected by 230 votes – the largest defeat for a sitting government in history.
Now the prime minister has invited party leaders and other MPs to discuss what needs to be done to reach Parliamentary consensus on any future deal.
However, she has been criticised for her unwillingness to compromise or alter her red lines.
Corbyn’s red line
Mr Corbyn has said that before any “positive discussions” can take place, the prime minister should rule out a no-deal Brexit.
The BBC’s political editor Laura Kuenssberg said it wasn’t a straightforward judgement for the Labour Party, as many members do not want Brexit to happen – meaning Mr Corbyn could be criticised for helping the process if he attends.
The views from other parties
The Lib Dems, the SNP and Plaid Cymru all spoke with Mrs May on Wednesday.
The SNP’s Westminster leader, Ian Blackford, said that the extension of Article 50 – the mechanism that allows the UK to leave the EU – the ruling out of a no-deal Brexit, and the option of a second EU referendum would have to form the basis of future discussions.
Plaid Cymru’s Westminster leader, Liz Saville Roberts, said they were “committed to finding a real solution” but “that means taking a no deal Brexit off the table and a People’s Vote on our European future”.
Liberal Democrat leader Sir Vince Cable said he was encouraged by Mrs. May’s “willingness to talk about these issues in detail”. The preferred choice of the party is another referendum.
But there remains deep division among Mrs. May’s own MPs – including within her cabinet – about possible compromises, such as the option of staying in a customs union.
The Times newspaper claimed Leader of the House Andrea Leadsom and other cabinet Brexiteers want Mrs. May to present MPs with a “Plan B” on Monday that would include a promise to impose a time-limit on the Northern Irish backstop – the fallback plan to avoid any return to physical border checks between the country and Ireland – and to negotiate a Canada-style free trade deal.
And the Telegraph reported it had seen a leaked transcript of a conference call in which Chancellor Philip Hammond told business leaders that a no-deal Brexit could be “taken off the table”.
Mrs. May has insisted she will “deliver on the verdict of the British people” and that she is seeking the “widest possible views across parliament” on a Brexit deal.
She said: “I am disappointed that the leader of the Labour Party has not so far chosen to take part, but our door remains open.”
Calls for new referendum
Meanwhile, Mr. Blackford has also written to Mr Corbyn, along with other opposition leaders, to urge him to back another referendum as Labour’s official position.
And, in a letter published in the Times newspaper, more than 170 leading business figures called for Theresa May and Jeremy Corbyn to back a second referendum on withdrawal from the European Union.
“The priority now is to stop us crashing out of the EU with no deal at all.
“The only feasible way to do this is by asking the people whether they still want to leave the EU… politicians must not waste any more time on fantasies. We urge the political leadership of both the main parties to support a People’s Vote,” it said.