Theresa May is to continue meeting with MPs from all sides in a bid to find a way forward for Brexit, following her slim victory in the no-confidence vote.
Speaking after talks with the Lib Dems, the SNP and Plaid Cymru on Wednesday, the PM said she wanted to approach the discussions in a “constructive spirit.”
But Labour leader Jeremy Corbyn has refused to join talks unless the threat of a no-deal exit is ruled out.
Mrs May must present a new plan for EU withdrawal to Parliament by 21 January.
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On Wednesday night, she called on MPs to “put self-interest aside” and “work constructively together” to find a way forward for Brexit.
“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 which rejected her withdrawal deal earlier this week – on Thursday.
Britain is due to leave the European Union on 29 March.
The prime minister won a vote of no confidence by 325 to 306, a margin of 19 votes.
She only survived thanks to the backing of the 10 members of the DUP.
Had they switched allegiance, the government would have lost by one vote: 315 to 316.
The vote came after MPs voted against Mrs May’s plans for Brexit on Tuesday night by an historic margin when it was rejected by 230 votes – the largest defeat for a sitting government in history.
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 and said the meetings she had held so far had been “constructive”.
However, she has been criticised for her unwillingness to compromise or alter her red lines.
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 quite easily be criticised for helping the process if he attends.
The Lib Dems, the SNP and Plaid Cymru all spoke with Theresa May on Wednesday.
Westminster leader of the SNP, 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”.
The leader of the Liberal Democrats, 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 a second referendum.
MPs on both the Remain and the Leave wings of the party have warned Mrs May she needs to make major changes to the deal if she is to get it through the Commons.
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 which 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 that 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.”
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.