Theresa May has accused Labour of dragging its feet over cross-party Brexit talks as MPs return to Westminster after the Easter break.
The prime minister said the Labour Party was engaging in the talks in a “serious” way but said there were difficulties with scheduling the talks.
Jeremy Corbyn said the lack of progress was due to the government’s refusal to compromise.
“They cannot keep on just regurgitating what has already been emphatically rejected three times by Parliament, there’s got to be a change,” the Labour leader said.
Mrs May remains under considerable pressure from her own backbenchers, who remain largely dissatisfied with her leadership.
Officers of the 1922 backbench committee met on Tuesday evening to discuss changing the party’s rules.
A rule change could allow MPs to challenge Ms May’s position as leader as early as June.
Nigel Evans, the committee’s secretary said Theresa May should announce her resignation “today” in order to break the Brexit impasse.
“I hope she does accept the fact the call for her resignation now is growing into a clamour,” he said.
But prisons minister Rory Stewart backed Mrs May as “our best hope” of resolving Brexit.
He told BBC’s Today programme that “the problem is not the Prime Minister, the problem is Brexit”.
If you would like to see how the day in Westminster unfolded please see what was our live coverage below:
The joint executive secretary of the 1922 Committee told the BBC Today programme the Conservatives need new leadership and that the process "can't start soon enough".
Mr Evans said: "To be honest I would be delighted if she announced today she was announcing her resignation and we could then have an orderly election to choose a new leader of the Conservative Party.
"I believe the only way we're going to break this impasse properly is if we have fresh leadership of the Conservative Party...
"If there was an announcement today by the Prime Minister then of course we could start the process straight away."
He said: "I hope she does accept the fact the call for her resignation now is growing into a clamour.
"It's not now just within Westminster - we've heard the news that 70 chairs of Conservative Associations throughout the country have now said that they reluctantly have no confidence in the prime minister."
Mr Evans said, with 40% of Conservative councillors likely to support Nigel Farage's Brexit Party in the European elections, Ms May's position would be "totally untenable".
Brexit negotiations between the government and Labour will resume on Tuesday as Theresa May launches a fresh bid to break the deadlock in parliament and quash new attempts to oust her from office.
The prime minister’s deputy, David Lidington, and the Brexit secretary, Steve Barclay, will lead talks with Labour, including shadow Brexit secretary Sir Keir Starmer, in a new effort to find a cross-party solution to the current crisis.
They will be joined by government chief whip Julian Smith and Ms May’s chief of staff, Gavin Barwell.
He told Today that "the problem is not the prime minister, the problem is Brexit" and a new leader would not make a difference.
He said: "I think she is doing a very, very important job and she needs to get the first stage of Brexit done...
"The idea somehow that some new, fresh leader with extraordinary charm and nimble feet would be able to suddenly get the deal across the line is mistaken.
"It's nothing to do with the individual, it is that people disagree deeply over Brexit."
He admitted that "a lot of MPs are cross and impatient" but insisted Ms May should keep her job.
He said: "Going into a leadership battle with Brexit completely unresolved it would not only have enormous uncertainty for the country, but it would tear politics apart, because it would lead to this deep, deep polarisation between people who want to remain and people who want to leave with no deal and she is our best hope of resolving that."
Change UK is launching its European elections campaign in Bristol this morning.
The former Labour and Conservative MPs quit their parties in protest over Brexit and handling of antisemitism complaints on the Labour side.
Former Labour MP Chuka Umunna sets out why the party is striking out on its own, rather than forming a broad Remain coalition with other smaller parties.
Donald Trump's long-awaited state visit to the UK is expected to be announced on Tuesday, sources have said.
Mr Trump's official trip could be scheduled for early June according to reports, and follows a working visit he made to Britain last summer with his wife Melania.
Theresa May offered Mr Trump a state visit early in his presidency when she met the US leader for the first time in the White House in January 2017.
But it was repeatedly pushed back over fears of major protests. His visit is likely to draw demonstrations in the same way as his July 2018 trip and security is expected to be high.
More here:
The First Minister is reported to have requested time to address parliament during Wednesday afternoon about Scotland's future and a potential independence referendum.
Ms Sturgeon said in January that she would set out her timetable for another vote in a "matter of weeks", but remained tight-lipped in light of ongoing Brexit uncertainty at Westminster.
Before the parliament's recess, Ms Sturgeon revealed that she would set out her plans for a second Scottish independence referendum after "this phase of the Brexit negotiations".
With the EU granting a six-month extension of Article 50, the First Minister is now expected to elaborate on the SNP's plans ahead of the party's conference at the weekend.
A Scottish Parliament spokesman said that, if the First Minister had requested the opportunity to address MSPs, any rescheduling to Wednesday's business would be confirmed by lunchtime on Tuesday.
On Tuesday morning Ms Sturgeon was meeting with cabinet colleagues and no one from her office could be reached for comment.
A Scottish Government spokesman said: "The First Minister has made clear she will update the Scottish Parliament after the Easter recess."
Nicola Sturgeon is expected to give a statement to the Scottish Parliament about plans for Scottish independence on Wednesday.
The First Minister is reported to have requested time to address Holyrood tomorrow about Scotland's future and a potential independence referendum.
Ms Sturgeon said in January that she would set out her timetable for another vote in a "matter of weeks", but remained tight-lipped in light of ongoing Brexit uncertainty at Westminster.
Speaking at the campaign event, which you can watch in the post below, to announce five new candidates, he said the party was already "doing very well" with Conservative supporters.
The former Ukip leader said: "There are five million people that voted for Jeremy Corbyn and voted for Brexit as well and that's going to be our task.
"I think we will go on squeezing the Conservatives and squeezing Ukip down to virtually nothing.
"We're going to go after that Labour vote in a very big way."
"Should a request be made to address the Houses of Parliament, it will be considered in the usual way," a spokeswoman for the Speaker's Office said.
