BERLIN — As chancellor of Germany, Angela Merkel leads a nation that prizes fiscal rectitude and adherence to the rules, and, after pledging tens of billions in bailout programs for five years, has expressed scant sympathy for Greece’s demand for more financial help.

As de facto leader of Europe, Ms. Merkel faces a very different set of responsibilities, starting with maintaining European unity in general and holding the euro together in particular.

In the wake of Greece’s landslide vote on Sunday to reject bailout terms that had been offered by its creditors, Ms. Merkel now confronts greater pressure than ever to resolve those clashing sensibilities — a challenge that will test her leadership abilities and help determine Europe’s direction at a crucial moment.

“This has taken on a political dimension that far exceeds the economics,” said Jan Techau, director of Carnegie Europe, a research group based in Brussels. “This is now about all the basic tenets of European integration — the balances between the economic and the political, between toughness and solidarity, whether Europe is still an example in the world for peaceful resolution, whether the southeastern flank holds.”