British Prime Minister Theresa May launched a rescue mission for her ailing Brexit deal Friday, after the European Union rebuffed her request to sweeten the divorce agreement so she can win over hostile lawmakers at home.

EU leaders meeting in Brussels showed little appetite to resolve May's Brexit impasse for her, saying the British Parliament must make up its mind. The choice was either back the Brexit agreement or send Britain tumbling out of the bloc in March without a deal and into unknown economic chaos.

"There is one accord, the only one possible," French President Emmanuel Macron told reporters at the end of a two-day summit. He said it was "the British Parliament's time" to decide whether to accept or reject it.

May came to an EU summit in Brussels seeking legally binding changes to the agreement, but the bloc told her bluntly that a renegotiation was not possible. They offered only assurances they would seek to move swiftly on forging a new trade deal after Britain leaves the bloc on March 29.

Nonetheless, May told reporters in Brussels that she welcomed the EU's words — and that as formal conclusions of an EU summit, they "have legal status."

"There is work still to do, and we will be holding talks in coming days about how to obtain the further assurances that the U.K. Parliament needs in order to be able to approve the deal," May said.

European Commission President Jean-Claude Juncker accused Britain of failing to give detailed proposals on Brexit, saying it was "up to the British government to tell us exactly what they want."

May was filmed speaking sternly to Juncker as leaders arrived at Friday morning's session of the summit. She said they had had a "robust" exchange, while Juncker played down the tiff caught on camera where May remonstrated with him about his remark that Britain's position on Brexit was "nebulous."

May herself said she accepted it had not been personal and Juncker, calling her "a woman of great courage," joked that they had kissed and made up afterward.

Asked if there was more on offer from the EU, summit chair Donald Tusk said there was no question of new negotiations and that he had no mandate for more meetings. He added that he remained at the disposal of the prime minister over Christmas.

Tusk went out of his way to counter British media reports of May being "humiliated" on Thursday evening as leaders badgered her for clarity on what she wanted after surviving a bid this week by her own party to oust her.

"We have treated the prime minister with much greater empathy and respect than some British MPs, for sure," he told reporters.

Diplomats said May had exasperated EU leaders at a meeting on Thursday by failing to outline precise proposals for what she needed to push the deal through, and even at one point used her much-derided mantra of "Brexit means Brexit."

"If this is all she has for us, there is no point trying too hard now," one diplomat told Reuters. "She still needs to do her homework — maybe she'll come back in January with something concrete and then we will see.

"To say 'Brexit means Brexit' more than two years after it all started was what toughened the other leaders' stance," said the diplomat.

May's allies at home said the summit was a useful start, but the opposition Labour Party said May had failed and called to parliamentary vote on the deal that she postponed on Monday, fearing a heavy defeat, to be held next week.

Arlene Foster, leader of the Northern Irish Party that props up May's minority government, urged May to stand up to the EU and win legally binding changes to the deal.

On the currency market, sterling fell around a cent to about $1.26 US and looked set for its biggest drop in seven weeks.

May asked for political and legal assurances that the so-called Northern Irish backstop would be temporary, and urged the leaders to look at her track record of delivering results even when the odds looked stacked against her.

The backstop is an insurance clause obliging Britain to follow EU trade regulations until a better way is found to avoid a "hard border" between Britain's Northern Ireland and EU member Ireland.

"Over the last two years, I hope I have shown that you can trust me to do what is right, not always what is easy, however difficult that might be for me politically," May said, according to a senior British official.

May said she believed there was "a majority in Parliament who want to follow through on the referendum and leave with a negotiated deal," but cautioned that an accidental no deal was possible.

EU leaders quashed a line in an earlier draft of their statement that had held out the prospect further "assurances" could be given in January.

One person briefed on the exchanges said May was "grilled" by leaders. "Everybody asked: What exactly do you want?," he said. "She had no solid answers."

Diplomats said May indicated she would want to come back for a second bite of "assurances" with "legal force," and some said they would be willing to listen and try to accommodate her.

But leaders also warned that the EU was prepared for Britain to leave without a deal rather than risk unraveling its own system of close integration:

"We have postponed the showdown moment. It will come back in January," one EU diplomat said.