Labour leader Jeremy Corbyn has expressed his frustration that the Government is not "moving off their original red lines" so the two parties can "reach a compromise" over Brexit.
Mr Corbyn said he had held a meeting of the shadow cabinet to discuss the Brexit talks with the Government.
However the Labour leader said there had been no movement on key issues in order to "secure an agreement."
Mr Corbyn said he had put forward a case for a customs union, alignment with the single market and full dynamic alignment of workers' rights, environmental protections and consumer standards.
He said: "Talks have to mean a movement and so far there has been no change in those red lines."
"We are looking for movement. Because we do not want to see a crashing out of the EU with no deal," Mr Corbyn added.
The Labour party and the Government will continue "technical talks" on Monday evening to try and break the Brexit impasse.
Time is running out for Theresa May to reach a Brexit compromise with Labour ahead of a summit with European leaders this week.
In a bid to reach a deal with the EU, Mrs May will travel to Paris and Berlin on Tuesday, following telephone conversations with European leaders on Monday to meet German Chancellor Angela Merkel and French President Emmanuel Macron in their national capitals.
With no Cabinet meeting scheduled for this week, Mrs May's attention is now focused on convincing European leaders she is trying to find a way forward.
Downing Street has said it hopes cross-party talks between the Conservatives and Labour will continue on Monday as the Government looks to forge a Brexit agreement Parliament would pass.
On Monday morning, Labour's shadow Brexit secretary, Keir Starmer, said the "ball is in the Government's court," and his party is waiting on it to put forward a resolution amicable to both sides of the table.
Speaking in Luxembourg on Monday, Jeremy Hunt told reporters Theresa May is "leaving no stone unturned" as the Tories try to get Brexit "over the line".
Mrs May has told European Union leaders she wants a delay to Brexit until June 30 at the latest, with the possibility of an early exit if she can get a deal through Parliament.
She has previously asked for an extension to June 30, but was instead told she could have until May 22 if MPs passed her deal in the Commons (which they have since rejected), or she provides a credible alternative by Wednesday, otherwise the UK will leave the EU on Friday.
EU Chief Negotiator Michel Barnier travelled to Dublin for talks with Leo Varadkar ahead of Wednesday's EU27 summit.
Mr Barnier said: "One thing is certain, whatever happens, the EU will stand fully behind Ireland, as I've said before the backstop is currently the only solution we have found to maintain the status quo on the island of Ireland.
Mr Barnier expressed hope that Conservative and Labour talks in London on a Brexit compromise would reach a "positive outcome" and said the EU's 27 member states would remain fully united.
"If the UK were to leave the EU without a deal we would not discuss anything with the UK until there is an agreement for Ireland and Northern Ireland as well as for citizens' rights and the financial settlement."
Leo Varadkar also said he is "open to extending the Brexit deadline" to allow time for discussions to run their course.
However International Development Secretary Penny Mordaunt said she "always believed that a customs union was not the best deal for the United Kingdom".
She also urged MPs to "pass the Withdrawal Agreement" before adding it is the only way to honour the result of the referendum.
Earlier on Monday, shadow Brexit secretary Sir Keir Starmer said: "everyone is hoping" Brexit talks between the two parties will continue. He added at the moment the "ball is in the Government's court," in terms of what is being negotiated, but there has not yet been a "change of position" from them.
Filmed at Chequers, the Prime Minister appeared relaxed as she acknowledged she could not see Parliament "accepting" her Withdrawal Agreement after rejecting it three times, and said MPs would not agree to a no-deal exit – currently the default position at 11pm on Friday unless an extension is granted.
As a result, she said, the Government were trying to find a "new approach" through cross party talks, but this would involve "compromise on both sides but I believe that delivering Brexit is the most important thing for us".
At the end of last week, negotiations between the two parties stalled after Labour said the Prime Minister had refused to set out any changes to her Brexit red lines and no further face-to-face meetings have yet been confirmed.
The current sticking point in Brexit negotiations is thought to be over a customs union, Labour's key demand to protect the flow of goods, but Brexiteers vehemently oppose anything that would restrict the UK's ability to strike free trade deals through being bound by tariffs set by the EU.
Downing Street has dismissed as "speculation" reports Mrs May could cave in over Labour demands for one, in a bid to come to an agreement.
If no deal can be reached with Labour, Mrs May has committed to putting a series of Brexit options to the Commons and being bound by the result.
One of the Government's legal advisers, Solicitor General Robert Buckland, told BBC Radio 4’s Westminster Hour that a customs union “does mean that we deliver an end to freedom of movement and it does mean that we deliver the vast majority of the aims of Brexit, which was to leave the institutions of the European Union”.
“It’s not perfect but, frankly, in this particular hung Parliament none of us can get perfection, we need to compromise.”
He said that “something approximating a customs arrangement or customs union would be the most likely outcome” of the process.
But former foreign secretary Mr Johnson used his Daily Telegraph column to warn that Tory MPs would not allow Mrs May to “surrender” to Mr Corbyn.
“If the UK were to commit to remaining in the customs union, it would make a total and utter nonsense of the referendum result,” he said.
“To agree to be non-voting members of the EU, under the surrender proposed by Jeremy Corbyn – it cannot, must not and will not happen.”
What are the main Brexit dates this week?
In a further sign of the constraints on Mrs May, Brexiteer Cabinet minister Penny Mordaunt warned a long delay to Brexit would be unacceptable to the public and businesses which were already “having to prepare for a whole raft of eventualities”.
“For me, the critical thing is that we leave, we do it swiftly, we don’t get locked into fighting European elections,” she told City AM.
“Brexit is something we have to do to arrive at where the public wanted to be, which is to have more control over laws, borders, money and trade, and having an independent trade policy.”
On Monday, peers will continue considering Yvette Cooper’s Bill forcing the Prime Minister to request a Brexit extension rather than leave the EU with no deal.
The Bill, which gives MPs significant power over the Brexit process, scraped through the Commons by a single vote last week.