EU leaders will have to decide whether to continue pressing for immediate negotiations on the terms of Britain’s withdrawal or to let passions cool in the hopes that some kind of deal might be worked out to keep Britain in the bloc.

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LONDON — The crisis ritual that will play out this week in Europe is all too familiar: Markets will gyrate. National leaders will huddle. A summit meeting in Brussels will extend deep into the night.

Until now, these tense moments have typically been resolved with vague statements of unity, awkward compromises and a determination to muddle through without any fundamental change in direction — until the next crisis comes along.

But Britain’s vote to leave the European Union (EU) presents the Continent’s leaders with difficult choices that may not be so easily kicked down the road or papered over.

“They can’t pretend nothing happened,” said Franco Pavoncello, a political analyst in Rome. “If they do that, the risk of further breakup and even disintegration of the euro might increase.”

Chancellor Angela Merkel of Germany, President François Hollande of France and Prime Minister Matteo Renzi of Italy will meet Monday in Berlin, and again with the heads of all 28 EU members in Brussels on Tuesday and Wednesday. The leaders will have to decide whether to continue pressing for immediate negotiations on the terms of Britain’s withdrawal or to let passions cool in the hopes that some kind of deal might be worked out to keep Britain in the bloc.

They will have to decide whether the lesson to draw from the British vote is that the growing populist and nationalist backlash against the bloc needs to be acknowledged through fundamental changes or whether it requires a show of resolve by pushing ahead with plans for deeper integration.

And they will confront the potential for a change in the power dynamic among the bloc’s biggest members, with Italy and to a degree France challenging the dominance of Germany and Germany’s insistence on austerity economics as the cornerstone of European policy.

In an op-ed published Sunday in Italy’s leading business newspaper, Il Sole 24 Ore, Renzi described the British vote as “an interesting opportunity to relaunch the European project.” He suggested that it was time for the bloc to focus on economic growth and job creation rather than debt reduction.

“It needs to take back its identity,” Renzi wrote of the EU. Austerity policies have “transformed the future into a threat,” he said, adding, “They spurred fear.”

Europe will be working its way through all those issues as Merkel, Hollande and Renzi, among other leaders, face intense political problems at home, undercutting their influence and restricting their room to maneuver. Merkel and Hollande are facing general elections next year, and Renzi’s fate could hang on a referendum on a new government structure in Italy this fall.

“Brexit raises a question mark for the whole planet,” Hollande said during the weekend. Struggling with poll ratings of 15 percent, he took the unusual step of inviting his archrivals, the conservative former President Nicolas Sarkozy and the nationalist leader Marine Le Pen, to lyse Palace to discuss the way forward.

“This vote is a brutal shock — now the whole world fears a populist shock wave,” the French foreign minister, Jean-Marc Ayrault, told the Sunday newspaper Le Journal du Dimanche. “We have to move quickly and show we understand the message of the people.”

Calls in France for a referendum on the EU mounted from both the far right and the far left, echoing sentiment in many other nations. The prospect of spreading political chaos may bind the German, French and Italian leaders together when they meet in Berlin on Monday. There is talk of a Franco-German effort to breathe life into the Continent’s key relationship with some sort of joint project, perhaps in defense — a field where Britain also remains deeply bound into the Continent through its membership in NATO.

Pavoncello suggested that a more likely vehicle for united European action was a restructuring of the EU, centered on the founding members — Belgium, France, Germany, Italy, Luxembourg and the Netherlands — with different levels of membership on the perimeters.

It is not clear whether such actions would help build bridges among ordinary Europeans who feel alienated by globalization and leaders who often seem out of touch with the concerns of their citizens.

Officials in Brussels and in the European Parliament pushed for quick negotiations on Britain’s exit, even as Merkel, Europe’s most powerful leader, said she saw no need to rush.

But Norbert Roettgen, a Merkel ally and the chairman of the foreign affairs committee of the German Parliament, noted that not even the Germans could afford complacency, especially with elections coming by the fall of next year. “If we go on like this,” he said in an interview, “the erosion will continue.”