But Labour accused the Prime Minister of failing to show “good faith” by insisting that she will not drop her negotiating red lines.
Labour leader Jeremy Corbyn is refusing to meet Mrs May until she takes the prospect of a no-deal Brexit off the table, and was instead going on the offensive by delivering a speech in a marginal Conservative constituency.
A Conservative “Right to Vote” campaign for a second EU referendum was launched by MP Phillip Lee, who claimed support for a so-called People’s Vote was “growing fast” among his colleagues on the Tory benches.
After seeing off a vote of no-confidence in her Government on Wednesday, Mrs May invited the other party leaders for individual talks to find a way forward on Brexit.
But she told the House of Commons she was holding to the “principles” behind the Withdrawal Agreement which was roundly rejected by MPs on Tuesday, including control of borders, laws and money and an independent trade policy.
Aides later said that the requirement for an independent trade policy was incompatible with membership of a European customs union - something which Labour regards as essential.
Shadow cabinet minister Barry Gardiner said Mrs May was clinging to her red lines because she knew that any compromise on them would “break the Conservative Party” by pushing eurosceptic backbenchers in the European Research Group (ERG) to desert her.
“If she wants to negotiate with all parties in Parliament, and if she wants to do that in good faith, she has to say ‘OK, I’m not sticking to every single one of the red lines that I’ve established’,” he told ITV’s Good Morning Britain.
“Take no-deal out of the equation and let’s get down to doing a solid deal.”
Mr Gardiner said that neither Mr Corbyn nor his frontbench team were taking part in discussions with the Government while no-deal remained on the table.
And he criticised Liberal Democrat leader Sir Vince Cable, the SNP’s Ian Blackford and Plaid Cymru’s Liz Saville Roberts, who met the PM on Wednesday evening, for “not sticking to the principles they have espoused”.
But Labour’s former prime minister Tony Blair said Mr Corbyn was wrong to snub the talks, telling BBC Radio 4’s Today: “If, in a moment of national crisis, the Prime Minister asks the Leader of the Opposition to come and talk, of course he should.”
In a live television address late on Wednesday evening, Mrs May said talks had been constructive, adding: “I am disappointed that the leader of the Labour Party has not so far chosen to take part, but our door remains open.”
And Conservative chairman Brandon Lewis said: “I am disappointed to see Labour again yesterday trying to frustrate and avoid Brexit by hanging open that they would possibly go for a second referendum.”
Mr Lewis told Today that remaining in a customs union was “something that people would feel is not delivering Brexit”.
Mrs May met Green MP Caroline Lucas on Thursday morning and was due to see groups of MPs representing different bodies of opinion during the day, including eurosceptic Tories and members of the Democratic Unionist Party. Meanwhile, Cabinet ministers were reported to be talking to their opposite numbers.
Sir Vince said it was “positive” that Mrs May had expressed a willingness to carry on talking after he told her that his party wanted the prospect of no-deal taken “off the table” and a second referendum.
“The fact that my team are willing to continue talking to her team of senior ministers this morning suggests that at least there is a willingness to explore these things,” the Lib Dem leader said.
Mrs May is expected to maintain an intensive round of meetings and phone calls before setting out her Plan B on Monday, in a Commons motion which crucially can be amended by MPs.
Amendments are expected to be tabled to seek parliamentary support for a range of options, from ruling out no-deal to extending the two-year Article 50 process or calling a second referendum.
It emerged that Chancellor Philip Hammond told business leaders on Tuesday that the 230-vote defeat for Mrs May’s plans had raised the question of whether a no-deal Brexit could now be taken off the table.
And a transcript of the call, obtained by the Daily Telegraph, recorded that the Chancellor said an amendment expected to be tabled by Tory backbenchers including Nick Boles on Monday could pave the way for Parliament to vote to “rescind” Article 50.
Though he acknowledged that the Government was “not in control” of events on Monday, Mr Hammond stressed: “It is not within their power to mandate any future course of action, that would be for a Government to do.”
Mr Boles’s EU Withdrawal (Number 2) Bill aims to put Parliament in control of the Brexit process, demanding an extension to the Article 50 process to allow negotiations to continue beyond the scheduled date of Brexit on March 29.
He last night withdrew proposals for the cross-party Commons Liaison Committee of senior backbenchers to draw up an alternative Brexit plan, after its chair Sarah Wollaston indicated that it would not accept the role.
French President Emmanuel Macron played down the prospect of changes to the offer from the EU27, saying: “We’ve reached the maximum of what we could do with the deal and we won’t, just to solve Britain’s domestic political issues, stop defending European interests.”
As the “first losers” from a no-deal Brexit would be the British people, he predicted that Mrs May would eventually ask for an extension of Article 50 for more negotiations rather than allow the UK to crash out on March 29.
Accusing Leave campaigners of misleading voters about the kind of Brexit they could obtain, Mr Macron said: “Good luck to the representatives of the nation who has to implement a thing which doesn’t exist and has to explain to the people: you have voted on a thing, we lied to you.”