Leaving the European Union with no deal would have a “very adverse” effect on the UK, the justice secretary has said.
David Gauke said he hoped a deal would be struck within the next 10 days, but if not the government should “act responsibly”.
But DUP deputy leader Nigel Dodds has insisted no deal was better than a bad deal.
Prime Minister Theresa May is seeking changes to the Withdrawal Agreement to help it achieve Parliamentary assent.
Mr Gauke warned on BBC Radio 4’s Today programme of “very grave concerns” for the UK’s economy, security and the union itself if the UK leaves without a deal.
“Leaving without a deal would have a very adverse effect, to put it mildly, on our economy, on our security and on the integrity of the union,” he said.
The justice secretary said he hoped a deal will have been struck by 27 February, when the next round of Brexit votes are scheduled in the Commons.
But he continued: “If not, then we will have to act responsibly and make sure the economy is protected, our security is protected and the integrity of the union is protected.
“I have very grave concerns about the consequences of leaving without a deal.”
Mr Gauke has previously suggested Brexit might have to be delayed.
But Mr Dodds told a meeting of party members in Omagh: “We want a Brexit deal, but we are very clear that a no deal is better than a bad deal.”
The DUP deputy leader said changes were needed to the so-called Brexit backstop.
The backstop is an insurance policy designed to avoid a hard border between Northern Ireland and the Irish Republic – and the Tories rely on DUP votes to govern.
Mr Dodds said that there is “virtual unanimity in political unionism” that the current backstop imperils the UK.
Meanwhile, Business Minister Richard Harrington said he did not think Theresa May would let Britain leave the bloc without a deal.
He told BBC Radio 4’s Week In Westminster: “When it comes to it, she will know the disaster that a hard Brexit would be for the British economy and I don’t think she’ll do it.
“No government can stand by and watch a country plummet earthwards because of a political dogma of a minority of a minority.”
And Margot James became the latest cabinet member to threaten resignation over the possibility of no deal.
The digital minister told Channel 4 News: “I could not be part of a government that allowed this country to leave the European Union without a deal.”
The prime minister is soon to return to Brussels to press for changes to the backstop. The EU has consistently ruled out amending the clause.