Theresa May has accused Labour of dragging its feet over cross-party Brexit talks as discussions resumed following an 11-day Easter break.
The Prime Minister acknowledged that Jeremy Corbyn's party was approaching the talks in a "serious" way but said they had hit difficulties over timetabling, with Conservatives pressing for greater urgency.
With Conservative MPs openly calling for Mrs May to name a date for her departure as PM, Downing Street is desperate to secure agreement in time to prevent European Parliament elections next month.
Officers of the Tory backbench 1922 Committee were meeting in Westminster on Tuesday evening to consider proposals to change party rules to allow MPs to challenge Mrs May's position as leader as early as June.
Meanwhile, the Remain-backing Change UK unveiled Boris Johnson's sister Rachel and former BBC correspondent Gavin Esler as candidates for the May 23 Euro elections while Nigel Farage announced former communist Claire Fox would stand for the Brexit Party.
At the first meeting of Cabinet since the Easter recess, ministers discussed the progress of cross-party talks, including the impasse over Labour's insistence on future involvement in a customs union with the EU.
Mrs May's official spokesman told reporters: "The Prime Minister said discussions with Labour had been serious but had also been difficult in some areas, such as in relation to the timetable for the negotiations.
"The PM said the Government's position was that progress needed to be made urgently as it was vital to deliver on the result of the referendum and for the UK to leave the European Union as soon as possible."
Mr Corbyn, however, put the blame for lack of progress on the Government's refusal to shift on its "red lines".
"We'll continue putting our case but quite honestly there's got to be change in the Government's approach," said the Labour leader.
"They cannot keep on just regurgitating what has already been emphatically rejected three times by Parliament, there's got to be a change."
He added: "What we're saying is that there must be a dynamic relationship, protection of rights at work, rights on what we consume and protection of our natural world as well as, of course, access to markets... and a customs union which would ensure there is no hard border in Northern Ireland.
"People might have voted to leave or to remain in the referendum nearly three years ago – they didn't vote to lose their jobs, they didn't vote to have a de-regulated society."
Talks at the Cabinet Office involved Mrs May's effective deputy David Lidington, Brexit Secretary Stephen Barclay and chief whip Julian Smith on the Government side, and shadow Brexit secretary Sir Keir Starmer, shadow chancellor John McDonnell, along with shadow cabinet ministers Rebecca Long-Bailey and Sue Hayman for Labour.
The Government faces a race against time to ratify a Brexit agreement in time to cancel the European elections.
It is thought that it may seek to accelerate progress by tabling the Withdrawal Agreement Bill (WAB) in the Commons as early as next week, even if cross-party talks have not reached a conclusion.
Ministers are wary of putting the bill before MPs unless they are confident of getting it safely through the Commons. WAB is the bill which ratifies the UK's Brexit agreement and its passage is essential for EU withdrawal.
If it is defeated, it cannot be retabled unless the Government brings the parliamentary session to an end and presents a new legislative programme in a Queen's Speech, introducing delays which would almost certainly dash hopes of avoiding the European elections.
Senior Conservative backbencher Nigel Evans called on Mrs May to announce her resignation to allow a contest to choose her replacement to begin "straight away".
The joint executive secretary of the backbench Tory 1922 Committee told BBC Radio 4's Today programme that the "severe problems" over Brexit meant Mrs May had to go "as soon as possible".
He said: "I hope she does accept the fact the call for her resignation now is growing into a clamour.
"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."
But prisons minister Rory Stewart backed Mrs May as "our best hope" of resolving Brexit.
He told Today that "the problem is not the Prime Minister, the problem is Brexit".
Mrs May has come under heavy criticism for her handling of the Brexit process, but survived a vote of confidence by her MPs in December by a margin of 200-117.
Under party rules, a year has to pass before another vote can be called. But it is understood the 1922 Committee executive is considering proposals to reduce this grace period to six months, permitting another challenge on June 12.
Some 70 local Conservative association chiefs have signed a petition calling for an extraordinary general meeting of the National Conservative Convention to discuss the Prime Minister's leadership of the party.
A confidence vote at the meeting would be non-binding but would put pressure on the 1922 Committee to find a way of forcibly removing the PM from office.
One of the petition's signatories, Greig Baker of Canterbury Conservatives, told BBC Radio 4's World at One: "Removing Theresa May has become like a trip to the dentist. It's something that's got to be done, and the longer you leave it the worse it will be."