Foreign Secretary Jeremy Hunt has urged EU leaders to "step back from the abyss" of a no-deal Brexit and engage with Theresa May's Chequers plan.
Following clashes at the Salzburg summit on Thursday, Mr Hunt added it was 'counterproductive' to 'insult' Britain's referendum vote and slammed claims that the only way the UK could legally leave was by "breaking up your country".
"What we need to be doing in a situation like this is bringing people together," he told the BBC Radio 4 Today programme.
"This is a time for people in the EU to step back from the abyss, to sit down and to talk to us about how we can make these sensible, concrete proposals actually work."
The foreign secretary also warned there would be 'disruption' on both sides of the Channel should the difficult negotiations lead to a tumultuous Brexit.
Some figures suggest that a million jobs could be lost across the EU should this be the case.
"What Theresa May is saying is 'Don't mistake British politeness for weakness.
"If you put us in a difficult corner we will stand our ground. That is the kind of country we are,"' he added.
"Insulting her on social media, getting to these stand-offs where you are calling people liars and so on is not the way we are going to get a solution to this difficult situation."
Mr Hunt also refused to rule out the government seeking a simple free trade agreement similar to Canada's to placate the many Tory MPs who would prefer this to Mrs May's more ambitious Chequers plan.
"We think these proposals are better than the Canada proposals because they work better on the Northern Irish border."
Donald Tusk had offered a conciliatory tone in response to Theresa May's statement on Friday where she said the UK and the EU are "at an impasse" in Brexit negotiations.
After ripping apart the Prime Minister's Chequers plan in Salzburg, the European Council president said today he "will treat the Chequers plan as a step in the right direction."
His rejection of Mrs May's plan was due to her "surprisingly tough and in fact uncompromising" stance.
In a statement, he said: "The UK stance presented just before and during the Salzburg meeting was surprisingly tough and in fact uncompromising.
"The response of the EU27 leaders was to reiterate our trust in chief negotiator Michel Barnier and to reiterate our position on the integrity of the Single Market and the Irish backstop.
"While understanding the logic of the negotiations, I remain convinced that a compromise, good for all, is still possible. I say these words as a close friend of the UK and a true admirer of PM May."
Hours earlier in a strongly-worded statement at Downing Street, Mrs May said her plan had been rejected by Mr Tusk without him properly explaining why it was unacceptable or offering an alternative.
She said the UK has "treated the EU with nothing but respect" during the negotiations and "the UK expects the same", adding : "A good relationship at the end of this process depends on it."
Mrs May said that at this late stage of the process it was "not acceptable" for one side to reject the other's proposals "without a detailed explanation and counter proposals".
"Donald Tusk said our proposals would undermine the single market. He didn't explain how in any detail or make any counter-proposal. So we are at an impasse."
- Watch Theresa May's statement in full:
The prime minister said there are two main issues where the EU and UK remain a "long way apart" in their negotiations: the future economic relationship and the Irish border.
She said EU proposals for the future economic relationship with the UK, whereby Britain would stay in the customs union and European Economic Area, would allow uncontrolled immigration from the bloc to continue and prevent the UK from making its own trade deals.
"That would make a mockery of the referendum," she said.
On the Irish border issue, she said: "We both agree that the Withdrawal Agreement needs to include a backstop to ensure that if there's a delay in implementing our new relationship, there still won't be a hard border between Ireland and Northern Ireland.
"But the EU is proposing to achieve this by effectively keeping Northern Ireland in the customs union. As I have already said, that is unacceptable. We will never agree to it. It would mean breaking up our country."
Mrs May said the Government would "do everything in our power to prevent a return to hard border".
She also reassured EU citizen living in the UK, saying that their rights would be protected in the event of no deal.
"You are our friends, our neighbours, our colleagues," she said. "We want you to stay."
Mrs May warned EU leaders that their approach to negotiations was "not acceptable" and said that the UK now needed clarity on their position.
"Until we do we cannot make progress," she said.
Mrs May concluded her statement with a defiant message, saying: "The EU should be clear, I will not overturn the result of the referendum, nor will I break up my country. We need serious engagement in resolving the two big issues in the negotiations and we stand ready."
It was a tough address by a Prime Minister needing to show a strong image ahead of the Conservative party conference next weekend.
- Video report by ITV News Political Correspondent Carl Dinnen
Labour leader Jeremy Corbyn said "political games" by the EU and the Government need to end "because no deal is not an option".
“Theresa May’s Brexit negotiating strategy has been a disaster," he said. "The Tories have spent more time arguing among themselves than negotiating with the EU.
“From day one, the Prime Minister has looked incapable of delivering a good Brexit deal for Britain."
Scottish First Minister Nicola Sturgeon has released a statement calling Mrs May's address "dreadful".
Ms Sturgeon said "Chequers is a dead duck but if her tactic now is to try and double down on those proposals and then seek to blame the EU for a no-deal outcome, then she will do huge damage to all of those she is supposed to serve."
Tory Brexiteer Jacob Rees-Mogg, who chairs the powerful European Research Group, welcomed the Prime Minister's "strong and forthright" speech but urged the Government to ditch Chequers and come forward with a Canada-style free trade agreement.
He said: "There is still no reason to suppose that Chequers can work either for the UK or the EU.
"It is time for the Government to start putting forward as its plan a Canada-style free trade agreement for the whole of the UK.
"This is the most realistic approach and similar to the EU's proposal."
He added: "The Prime Minister has shown steely resolve at the eleventh hour and is standing up to the EU bullies. The next step is to say to the EU £40 billion and free trade or World Trade terms."
Tom Brake, the Liberal Democrats spokesman for Brexit, called Mrs May's recent European summit "humiliating", adding that a no-deal Brexit is "more likely than ever".
The pound plummeted following Mrs May's speech, trading down 1.3% versus the US dollar at 1.31. Against the euro, sterling was down 1% at 1.11.