UK Prime Minister Theresa May said Friday that negotiations with the European Union were "at an impasse" after a disastrous summit at which her Brexit plan was largely rejected.

May struck a defiant tone during a Downing Street statement in which she called for the European Union to “respect” the British position and the result of the June 2016 referendum.

A day after returning from the summit in Salzburg, she called for the EU to spell out its objections to her plan or come up with an alternative.

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

Downing Street had hoped the informal Salzburg summit would pave the way to a resolution of outstanding issues in Brexit talks before a formal meeting in October.

Instead, the leaders of the 27 remaining EU nations were unexpectedly resolute in their opposition to her proposals. Donald Tusk, President of the European Council, said key aspects of the plan, agreed at the Prime Minister's Chequers country retreat in July, “will not work” in their current form.

French President Emmanuel Macron went even further, saying that the entire Brexit project was sold to the British people by “liars” who immediately fled the stage, unwilling to see their project through.

In her Downing Street statement, May refused to budge and said the ball was in the EU's court.

“At this late stage in the negotiations, it is not acceptable to simply reject the other side's proposals without a detailed explanation and counterproposals,” she said. “So we now need to hear from the EU what the real issues are and what their alternative is so that we can discuss them. Until we do, we cannot make progress. In the meantime, we must and will continue the work of preparing ourselves for no deal.”

May will face tough questions at her Conservative Party's annual conference, which begins September 30.

Amid the uncertainty over the negotiations, she has been plagued by outspoken criticism from within her own party, in particular from ardent supporters of Brexit, who believe she has not been tough enough with the EU.

Meanwhile, Remain supporters have been rallying behind a burgeoning campaign for a new referendum, known as a “people's vote.”