Cabinet minister Chris Grayling has said there will be no deal with the EU on Brexit if it does not soften its position on the Irish border.
His comments come after EU leaders rejected Theresa May’s Chequers plan at their Salzburg summit on Thursday.
EU chief Donald Tusk said a key part of that plan “will not work” but the prime minister said it was the only credible way to avoid a hard Irish border.
Mr Grayling told the BBC he was still confident a deal could be done.
He added that “tough language” was to be expected.
The UK is due to leave the EU on 29 March 2019.
Both sides are trying to reach a deal in time and want to avoid a hard border – meaning any physical infrastructure like cameras or guard posts – between Northern Ireland and the Irish Republic but cannot agree on how.
The EU insists on its own “operational and legally-binding Irish backstop” – what it describes as an insurance policy to prevent the return of physical infrastructure on the border in the event no other solution can be found.
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It has put forward a proposal that would see Northern Ireland stay aligned with the EU in key areas, effectively staying in the customs union and single market and not needing those border checks.
But the UK insisted this was unacceptable as it would split Northern Ireland off from the rest of the UK.
Mrs May says her Chequers proposal for the UK to sign up to a common rule book for trade in goods and a combined customs territory with the EU is the only way to avoid a hard border and breaking up the UK.
She has said the UK will come forward “shortly” with new proposals on the so-called “backstop” arrangements, but also insisted Chequers was the “only serious and credible proposition” for an overall deal.
By BBC political editor Laura Kuenssberg
Theresa May and her government have been trying to pursue a middle way, to find a stance between the basic options – a close “Norway style”, or free trade deal roughly like Canada.
It feels that the search for something else has been in vain.
Sources on the EU side express irritation at the UK’s approach, at what they see as the strident tone the prime minister took in the last 48 hours.
The European Council is not the same as Prime Minister’s Questions, it’s suggested.
But to kick out publicly as they did in Salzburg certainly runs the risk of pushing Mrs May too far.
Transport Secretary Mr Grayling told BBC Newsnight they had put forward the only proposal that meets the UK’s red lines and also provides the “right solution” for the Irish border.
“At the moment what the European Union is asking in and around Northern Ireland is simply impossible for any UK government to accept. And actually if they stick with that position, there will be no deal,” he said.
“No UK government, certainly not this one – and the Labour Party have said the same – could possibly accept any border in the Irish Sea, between Northern Ireland and the rest of the UK.”
He said the negotiation where people were setting out “robust, firm positions” was typical of the EU.
“They build up, there’s tough language and actually a deal is done at the last. And I’m still confident that we will reach agreement,” he said.
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Speaking to BBC Radio 4’s Today programme, Conservative MP Stephen Crabb said the EU’s attempts to “belittle” Mrs May would push people who have been advocating compromise with the EU to think “the quicker we’re out of this circus the better”.
But he added negotiations were not yet at an “end game” and said Chequers was “broadly” a package that could get through Parliament.
However David Davis, who quit as Brexit secretary after the Chequers plan was agreed by the cabinet, disagreed.
He told HuffPost UK that, with Labour also planning to vote against Mrs May’s plan, the “critical size of the voting bloc is quite small, it’s basically a dozen people”.
Mrs May set out her proposals for the key issue of cross-border trade after a Chequers summit in July, but it has been fiercely criticised by some Brexiteers who say plans for a “common rulebook” on goods would compromise the UK’s sovereignty.
On Thursday after a two-day meeting in Salzburg, Austria, Mr Tusk said EU leaders agreed the UK proposals needed to be redrawn.
He said: “Everybody shared the view that while there are positive elements in the Chequers proposal, the suggested framework for economic co-operation will not work, not least because it is undermining the single market”.
Mr Tusk added that October would be the “moment of truth” for reaching a deal, and that “if the conditions are there” an additional summit would be held in November to “formalise” it.
French President Emmanuel Macron said Brexit had been “pushed by certain people who predicted easy solutions”.
He added: “Brexit has shown us one thing – and I fully respect British sovereignty in saying this – it has demonstrated that those who said you can easily do without Europe, that it will all go very well, that it is easy and there will be lots of money, are liars.”
Prominent Conservative Brexiteer Jacob Rees-Mogg, said Mr Tusk’s remarks signalled the end for the Chequers proposals while Labour’s shadow Brexit secretary Sir Keir Starmer said Mrs May had to “urgently drop her reckless red lines and put forward a credible plan for Brexit”.