Theresa May has urged Jeremy Corbyn to discuss his Brexit plans with her, after he said he would not take part in talks until "no deal" was ruled out.
In a letter to the Labour leader, the PM wrote that ruling out no deal was an "impossible condition" as it was not within the government's power to do it.
She has been meeting other leaders to try to find a compromise on Brexit after her deal was rejected by MPs.
Earlier, Mr Corbyn dismissed the talks as a "stunt".
The PM will publish a new plan on Monday with a full debate and key vote scheduled for Tuesday, 29 January.
Senior politicians on all sides have also been meeting with cabinet ministers to try to find a way forward.
But Mr Corbyn, the leader of the opposition, declined to take part, telling Mrs May to "ditch the red lines" and "get serious about proposals for the future".
What has Jeremy Corbyn said?
In a speech in Hastings Mr Corbyn said: "With no-deal on the table, the prime minister will enter into phony talks just to run down the clock and try to blackmail MPs to vote through her botched deal on a second attempt by threatening the country with the chaos that no-deal would bring."
Mr Corbyn said the "best outcome" was to call a general election to "break the deadlock".
The Labour leader has emailed Labour MPs urging them not to talk to Mrs May until she has ruled out a no-deal Brexit.
His stance has come under fire from Labour MP Mike Gapes, a longstanding critic of Mr Corbyn, who told BBC Radio 4's The World at One: "Jeremy Corbyn has been quite happy in the past to talk to Hamas, Hezobollah... I find it extraordinary he's not prepared to go and meet the prime minister."
What has Theresa May said?
In her reply, Mrs May said: "I note that you have said that 'ruling out' no deal is a precondition before we can meet, but that is an impossible condition because it is not within the Government's power to rule out no deal.
"Let me explain why. Under Article 50 of the Treaty on European Union and the Withdrawal Act 2018, we will leave the EU without a deal on 29 March unless Parliament either agrees a deal with the EU or the UK revokes article 50 and chooses to stay in the EU permanently.
"So there are two way to avoid no deal: either vote for a deal, in particular a Withdrawal Agreement, that has been agreed with the EU, or to revoke Article 50 and overturn the referendum result.
"I believe it would be wrong to overturn the referendum result."
She wrote that she would be "happy" to discuss Mr Corbyn's proposals.
On Wednesday night, speaking outside Downing Street after talks with the Lib Dems, SNP and Plaid Cymru, Mrs May called on MPs to "put self-interest aside".
"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.
Separately, Downing Street said the government has produced a "very short paper setting out the factual detail on the number of months required" to hold another EU referendum, which suggests it would take "in excess of a year".
The point of the document was to "inform the expected discussion" Mrs May was likely to have with MPs who back another public vote, government sources say.
Who is the PM meeting?
The prime minister is holding meetings with various party leaders as well as Tory Brexiteers and the DUP - both of whom rejected her withdrawal deal earlier this week - on Thursday.
Environment Secretary Michael Gove, Cabinet Office Minister David Lidington and Brexit Secretary Steve Barclay are also holding talks with senior opposition politicians, including Labour MPs Hilary Benn and Yvette Cooper.
What do MPs say happened in their meetings?
The SNP's Westminster leader, Ian Blackford, said that the extension of Article 50 - the two year mechanism that means the UK leaves the EU on 29 March - 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.
Party leader and Scotland's First Minister Nicola Sturgeon tweeted that the talks were just "time wasting" if the prime minister was not prepared to consider another referendum, rule out a no-deal Brexit or to extend Article 50.
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, who wants a referendum, said he was encouraged by Mrs May's "willingness to talk about these issues in detail".
Following her meeting on Thursday, Green MP Caroline Lucas said the PM refused to rule out a no-deal Brexit.
"I repeatedly urged her again and again to take 'no deal' off the table because I think it completely skews the talks because you know that cliff edge is there," she said.
Mrs May was also resisting the option of extending Article 50, Ms Lucas said.
DUP leader Arlene Foster said the prime minister was in "listening mode" and there was optimism that a Brexit deal could still be reached.
She said she made a "clear ask" in relation to the Irish backstop, urging Mrs May to address it "in a satisfactory way".
What is the view from the government?
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".
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.
What has the EU been saying?
EU's chief Brexit negotiator Michel Barnier has suggested that Brussels was ready to respond to any changes in Mrs May's "red lines", saying: "If they change, we'll change."
He said getting an agreement was "in everybody's interest" and that "something has to change" if it is to be secured.
What happened in the vote of no confidence?
The prime minister survived a vote of no confidence in her government by 325 to 306 votes - a margin of 19 - thanks to the backing of the 10 members of the DUP. Had they switched allegiance, the government would have lost by one vote.
Click here if you cannot see the look-up tool. Data from Commons Votes Services.
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.
Former prime minister Tony Blair told BBC Radio 4's Today that an extension to Article 50 was "inevitable" at this point and warned a no-deal Brexit would do "profound damage" to the UK's economy.
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".
Meanwhile, the SNP's Ian 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 another referendum on withdrawal from the European Union "to stop us crashing out of the EU with no deal at all".
Addressing a Leave Means Leave gathering in Westminster on Thursday evening, former UKIP leader Nigel Farage said Brexiteers should "prepare" and "organise" for the possibility of a another referendum.
"If I have to fight again against this lot... it's no more Mr Nice Guy," he said.