Downing Street has insisted it is prepared to pursue alterations to its Brexit deal and is ready to hold further talks with Labour this weekend.
Labour wants fundamental changes to the deal’s political declaration, which outlines future UK-EU relations.
But three days of talks ended without agreement on Friday, with Labour’s Sir Keir Starmer saying ministers were not “countenancing any change” to the text.
A Downing Street spokesman said: “We have made serious proposals.”
The government was “prepared to pursue changes to the political declaration in order to deliver a deal that is acceptable to both sides”, he added.
The political declaration sets out ambitions for the future relationship between the UK and EU after Brexit – including on trade, regulations, security and fishing rights – but does not legally commit either party.
Meetings have been taking place between Tory and Labour politicians to find a proposal to put to MPs which it is hoped can break the Brexit deadlock in the Commons before an emergency EU summit next week.
However, Sir Keir said the government’s approach had been “disappointing” and that it had refused to consider changes to the “actual wording” of the political declaration.
“We want the talks to continue and we’ve written in those terms to the government, but we do need change if we’re going to compromise,” the shadow Brexit secretary added.
Prisons minister Rory Stewart told BBC Radio 4’s PM programme there were “tensions” but insisted that both sides were very close and that there was “quite a lot of life” left in the talks.
BBC political editor Laura Kuenssberg said: “The sense is that the government has only offered clarifications on what might be possible from the existing documents, rather than adjusting any of their actual proposals in the two documents.”
She added that both sides agreed the talks are not yet over, but there were no firm commitments for when further discussions might take place.
The UK is due to leave the EU on 12 April and, as yet, no withdrawal deal has been approved by the House of Commons.
Many MPs believe leaving without a formal deal would create problems for businesses and cause difficulties at ports.
Prime Minister Theresa May has written to European Council President Donald Tusk to request an extension to the Brexit process until 30 June.
A senior EU source told BBC Europe editor Katya Adler that Mr Tusk would propose a 12-month “flexible” extension, with the option of the UK leaving sooner once Parliament had ratified a deal.
Any extension would have to be unanimously approved by EU leaders.
Irish Prime Minister Leo Varadkar said a longer delay to Brexit “might make more sense” than the UK seeking “an extension every couple of weeks or every couple of months, because that just adds to the uncertainty for citizens, for businesses and for farmers”.
However, French Europe minister Amelie de Montchalin said such a delay would require the UK to put forward a proposal with “clear and credible political backing”.
“In the absence of such a plan, we would have to acknowledge that the UK chose to leave the EU in a disorderly manner,” she added.
Mrs May says that if the Commons agrees a deal in time, the UK should be able to leave before European parliamentary elections are held on 23 May.
But the UK would prepare to field candidates in case MPs failed to back a deal, she said.
The prospect has angered many Conservatives, with prominent Brexiteer Jacob Rees-Mogg arguing: “If a long extension leaves us stuck in the EU we should be as difficult as possible.”