The government says “progress needs to be made urgently” on Brexit talks with Labour – but that arranging time with the opposition has been “difficult”.
Senior figures from both sides have been trying to break the deadlock by agreeing a Brexit deal MPs can support.
No 10 said talks had “been difficult in some areas”, including “timetabling”.
But Labour leader Jeremy Corbyn said the government “really needs to move on” and change its withdrawal agreement to solve the impasse.
He said: “We cannot go on hearing this tired old mantra that the Brexit agreement has to be adhered to.”
The deal Theresa May negotiated with the EU has been rejected twice by Parliament, with the withdrawal agreement – the terms on how the UK leaves the bloc, rather than its future relationship with it – defeated a further time.
Weeks of talks resumed between the two parties in Westminster on Tuesday afternoon following the Easter break.
Mrs May’s de facto deputy David Lidington was expected to lead for the government.
Shadow Brexit secretary Keir Starmer, shadow chancellor John McDonnell, shadow business secretary Rebecca Long-Bailey and shadow environment secretary Sue Hayman took part on behalf of Labour.
Ahead of the meeting, Sir Keir said “fundamental issues” remained between his party and ministers on a number of key issues.
Some Tory MPs are angry the discussions with Labour are even taking place.
Leading backbencher Nigel Evans called on Theresa May to step down as prime minister “as soon as possible”, adding that the PM “had been reaching out to the Labour Party and Jeremy Corbyn, when she should have been reaching out to the people”.
Timing seems to be a key issue.
The word is that Labour has engaged seriously in the talks, but on timing, they feel it will take longer than the next few weeks to reach some kind of agreement.
The PM, though, is still keen to avoid the UK taking part in the European Parliamentary elections.
The only way that could be done is if the deal passes Parliament before 22 May.
And nothing in the talks so far suggests that this tighter timeframe is definitely achievable.
Senior members of the influential 1922 committee of Tory MPs are meeting now in Parliament.
Under current party rules, MPs cannot call another no-confidence vote in the prime minister until December – but the 1922 are expected to discuss whether steps should be taken to try to change that.
The only way we’re going to break this impasse properly is if we have fresh leadership of the Conservative Party,” he said.
But Prisons Minister Rory Stewart said Theresa May was doing a “good job” and deserved “praise not blame”.
He added: “It’s nothing to do with the individual, it’s that people disagree deeply about Brexit.”
The comments came after it emerged that Mrs May faces a no-confidence challenge from Tory campaigners.
More than 70 local association chiefs have called for an extraordinary general meeting to discuss her leadership and a non-binding vote is to be held at the National Conservative Convention EGM in May.
If the grass-roots Tory vote showed a lack of confidence – it could put greater pressure on the 1922 Committee to find some way of forcibly removing the PM from office.
That pressure could increase further if the Tories poll badly in local and European elections on 2 and 23 May respectively.
The UK has been given an extension to the Brexit process until 31 October
Change UK has launched its European election campaign in Bristol, while Nigel Farage’s Brexit Party has unveiled more of its candidates in London.