As Chancellor Angela Merkel of Germany, President François Hollande of France and Prime Minister Matteo Renzi of Italy meet on Monday in Berlin, and again with the heads of all 28 European Union members in Brussels on Tuesday and Wednesday, they 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, Mr. 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,” Mr. Renzi wrote of the European Union. Austerity policies have “transformed the future into a threat,” he said, adding, “They spurred fear.”