BRUSSELS — After winning a confidence vote and saving her job for now, Prime Minister Theresa May of Britain on Thursday had less success in extracting concessions from European Union leaders who rebuffed her pleas to help her salvage an embattled agreement on leaving the bloc.

At a summit meeting in Brussels, Mrs. May appealed to the other 27 leaders to start crafting new and legally binding reassurances that could be crucial in winning over critics of her deal on British withdrawal, or Brexit, in Britain’s Parliament.

But while the European leaders offered some reassuring words, Mrs. May was told her ideas were too vague and she was given no promise of the new commitments that she thinks could unblock her domestic logjam.

“There will be no legally binding new obligations imposed,” said Jean-Claude Juncker, president of the European Commission, adding that “this is crystal clear.” There could, he said, be some clarifications “but there will be no renegotiation.”