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.
He said the UK would not abandon its Chequers plan, despite EU leaders rejecting it at their Salzburg summit.
EU chief Donald Tusk said a key part of that plan “will not work” but Theresa May said it was the only credible way to avoid a hard Irish border.
Mr Grayling told the BBC “tough language” was to be expected.
He said he was still confident a deal could be done.
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 “legally operationally 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.
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.
Theresa 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.
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.
However David Davis, who quit as Brexit secretary after the Chequers plan was agreed by the cabinet, suggested Mrs May’s plan would not get through the UK Parliament – where it has many critics in her own party.
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.
“The rock-solid core of the [European Research Group] is a multiple of that. I’m not even an ERG member. It’s probably 30, 40.”
But he added that Leave-backing Tory MPs were “reasonably terrified” of the possibility that Labour under Jeremy Corbyn could win an ensuing general election: “That’s what they [No 10] are banking on. We will see who blinks.”
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.
“This is all the more true because they left the next day, so they didn’t have to manage it.”
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”.
But DUP deputy leader Nigel Dodds blamed the EU for its “unreasonable and inflexible approach” adding: “The UK government must demonstrate a resolute determination not to be bullied.”