She was also asking for more time to solve the thorny issue of the border between Northern Ireland, which remains a part of the United Kingdom, and Ireland, which is a member of the E.U.

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May faces opposition from not only a hard-bargaining Europe, which does not want to make it too appealing for members to leave their club, but also her own Conservative Party, populated by hard-line Brexiteers such as former foreign secretary Boris Johnson, who disparages the prime minister’s exit plan as a weak capitulation to Brussels.

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Challenges to her Brexit plan and her leadership will take center stage at a raucous party conference in early October.

Her Salzburg trip did not help.

Speaking to the media in Salzburg on Thursday, French President Emmanuel Macron said staunch Brexit backers had deceived the British people, promising a windfall of funds and a painless exit.

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Brexit was pushed by those “who predicted easy solutions,” Macron said. “Those people are liars. They left the next day so they didn’t have to manage it.”

May had warned European leaders that her plan — agreed to by her divided cabinet in July at the prime minister’s official country manor, Chequers — was the only way forward. But Macron countered, “The Chequers plan cannot be take it or leave it.”

Donald Tusk, the European Council president, said May’s proposal to create a British-European free-trade regime covering agriculture and goods — but not services — was not acceptable.

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“There are positive elements in the Chequers proposal, but the suggested framework for economic cooperation will not work, not least because it risks undermining the single market,” Tusk said.

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The E.U.’s single market offers much to its members but also requires the free movement of people among its countries. Britain wants to control its own immigration and make its own trade deals.

Tusk said May has just four weeks to amend her plan — or perhaps face the dreaded prospect of leaving the European bloc with no deal — the so-called doomsday scenario.

German Chancellor Angela Merkel warned, “There is still a lot of work to do on the question of how future trade relations will look.”

Speaking of May’s proposals, Merkel said, “You can’t belong to the single market if you are not part of the single market, but you can develop a lot of creativity to find practical, good, close solutions.”

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