By JILL LAWLESS, Associated Press

LONDON (AP) — British Prime Minister Theresa May accused the European Union on Friday of creating an "impasse" in divorce negotiations by bluntly rejecting her blueprint for Brexit, sending the value of the pound falling as worries about a chaotic U.K. exit from the EU soared.

With British newspapers declaring that May had been "humiliated" by EU leaders, the prime minister used a televised statement from 10 Downing St. to insist she was prepared to take Britain out of the bloc without a deal if it did not treat the country with more respect.

Declaring that "we are at an impasse," May said the EU must lay out "what the real issues are and what their alternative is."

"Throughout this process, I have treated the EU with nothing but respect," she said. "The U.K. expects the same. A good relationship at the end of this process depends on it."

The pound fell 1.5 percent to $1.3066 on May's comments, which seemed to make the prospect of an economically disruptive "no deal" Brexit more likely.

May's strong words belied her weak position: She is a prime minister without a parliamentary majority, caught between the EU and a pro-Brexit wing of her Conservative Party that threatens to oust her if she makes a compromise too far.

May's combative remarks were calibrated to appease euroskeptic Conservatives ahead of what's likely to be a bruising annual party conference at the end of the month.

May's statement followed a fraught EU summit in Salzburg, Austria, which dashed hopes of a breakthrough in stalled divorce talks with only six months to go until Britain leaves the bloc on March 29.

European Council President Donald Tusk said at the meeting that parts of the U.K.'s plan simply "will not work." French President Emmanuel Macron called pro-Brexit U.K. politicians "liars" who had misled the country about the costs of leaving the 28-nation bloc.

The judgment of British newspapers was brutal. The broadly pro-EU Guardian said May had been "humiliated." The conservative Times of London said: "Humiliation for May as EU rejects Brexit plan."

The Brexit-supporting tabloid Sun branded bloc leaders "EU dirty rats," accusing "Euro mobsters" Tusk and Macron of "ambushing" May.

UK Brexit Secretary Dominic Raab said the bloc had "yanked up the handbrake" on the negotiations.

But despite all the heated British rhetoric, the EU's position was not new.

May's "Chequers plan" — named for the prime minister's country retreat where it was hammered out in July — aims to keep the U.K. in the EU single market for goods but not services, in order to ensure free trade with the bloc and an open border between the U.K.'s Northern Ireland and EU member Ireland.

EU officials have been cool on the plan from the start, saying Britain can't "cherry-pick" elements of membership in the bloc without accepting all the costs and responsibilities.

Yet British politicians and diplomats were taken aback by Tusk's blunt dismissal of the Chequers plan on Thursday — and by his light-hearted Instagram post showing Tusk and May looking at a dessert tray and the words: "A piece of cake, perhaps? Sorry, no cherries."

In a statement Friday, Tusk said the bloc's position had "been known to the British side in every detail for many weeks." He said EU leaders regarded Chequers as "a step in the right direction" but had been taken aback by May's "uncompromising" stance in Salzburg.

Tusk said in Salzburg that an EU summit on Oct. 18-19 would be the moment of truth, when an agreement on divorce terms and the outlines of future trade would be sealed or would fail.

The biggest single obstacle to a deal is the need to maintain an open Irish border. Failing to do so could disrupt the lives of people and business on both sides, and undermine Northern Ireland's hard-won peace.

Britain and the EU have agreed on the need for a legally binding backstop to guarantee there is no return to customs posts and other border checks. But Britain rejects the EU's proposed solution, which would keep Northern Ireland inside the bloc's customs union while the rest of the U.K. leaves.

May said Friday the EU was "making a fundamental mistake" if it believed she would agree to "any form of customs border between Northern Ireland and the rest of the U.K."

May said she wanted to reassure people in Northern Ireland "that in the event of no deal, we will do everything in our power to prevent a return to a hard border."

She also said more than 3 million EU citizens living in the U.K. would retain their rights even if Britain left the bloc without an agreement.

"You are our friends, our neighbors, our colleagues. We want you to stay," May said.

Dealing with the EU is only part of May's problem. Pro-Brexit Conservatives, including former Foreign Secretary Boris Johnson, hate the Chequers plan, saying it would keep Britain tethered to the bloc, unable to strike new trade deals around the world.

Conservative lawmaker Jacob Rees-Mogg, an arch-Brexiteer, praised May for "standing up to the EU bullies," but urged her to ditch the Chequers plan for a much looser "Canada-style" free trade agreement."

Pro-EU politicians don't like the Chequers plan either, saying it will cut the U.K.'s vast services sector out of the EU's single market. Many are pushing for a new referendum that would let voters choose between accepting whatever deal she manages to negotiate with the bloc and staying in the EU.

Labour Party Brexit spokesman Keir Starmer said May was "in denial."

"I don't understand why she's failed to hear the message that the Chequers proposal wasn't going to be accepted by the EU and frankly it's not going to be accepted by her own party," he said.

Despite the somber mood music, Britain and the EU hinted there could be a way forward.

"I remain convinced that a compromise, good for all, is still possible," Tusk said. "I say these words as a close friend of the U.K. and a true admirer of PM May."

May said a solution required "serious engagement on resolving the two big problems in the negotiations" — trade and the Irish border.

"We stand ready," she said.

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Associated Press writers Danica Kirka and Carlo Piovano contributed.