Theresa May will meet Jeremy Corbyn later to see whether there is common ground to break the Brexit deadlock, Brexit Secretary Stephen Barclay says.
He said the “remorseless logic” of MP numbers in the House of Commons meant the UK was heading for an “undesirable” soft Brexit – closer links with the EU.
There were no preconditions for the talks, he said, but it was not a “blank cheque” either.
Mr Corbyn says he wants a customs union and workers’ rights to be priorities.
BBC political editor Laura Kuenssberg said there was not much difference between the government’s version of Brexit and Labour’s version, but there did not seem to be “an enormous amount of confidence” a political consensus could be reached from either party.
The PM’s move to hold talks has angered some Brexiteers, with Wales Minister Nigel Adams resigning his role.
Mr Adams said the government was at risk of failing to deliver “the Brexit people voted for” and failing to prevent “the calamity of a Corbyn government”.
Prominent Brexiteer Boris Johnson has accused Mrs May of “entrusting the final handling of Brexit to Labour”.
And Jacob Rees-Mogg, leader of the Eurosceptic European Research Group (ERG) of Tory MPs, described the offer as “deeply unsatisfactory” and accused Mrs May of planning to collaborate with “a known Marxist”.
But Mr Barclay blamed hard Brexiteers in the ERG who refused to back the PM’s deal.
He told BBC Radio 4’s Today programme: “It’s regrettable that what we have been saying for several months now is coming to pass but that is the remorseless logic of not backing the prime minister’s deal.
“Because the alternative then is to have to seek votes from the opposition benches because 35 of my own colleagues would not support the prime minister’s deal.”
Mr Barclay said the consequence of MPs not passing the PM’s deal was either a “soft Brexit or no Brexit at all”.
“It [a soft Brexit] is undesirable but it’s the remorseless logic of the numbers of the House of Commons,” he said.
He said the EU has said the withdrawal agreement is the only deal available, but he said Labour had expressed more concern about the future relationship – which is contained within the separate political declaration.
The withdrawal agreement includes how much money the UK must pay to the EU as a settlement, details of the transition period, and citizens’ rights – as well as the controversial Irish backstop that aims to avoid a hard border on the island of Ireland.
The political declaration sets out proposals for how the UK’s long term future relationship with the EU will work after Brexit.
