BERLIN — Even Angela Merkel, the usually unruffled veteran of European crises after almost 11 years as chancellor of Germany, had to admit it last week: “The world finds itself in a critical condition,” she said, and there is no point “in painting anything rosier than it is.”

The outlook for Ms. Merkel is not especially rosy, either.

After years of broad and deep support at home, bolstering her as she grew to become the Continent’s most powerful leader, she is heading toward national elections next year more politically vulnerable than at any time since her early days in office, with implications that extend far beyond Germany’s borders.

When she arrives in Slovakia on Friday for a summit meeting of leaders from 27 European Union nations — all save Britain, which voted in June to leave the bloc — her ability to navigate her troubles at home will hang over the gathering.

Since Britain’s decision, other European governments have done little to respond to the surge in populism and nationalism across the Continent or to reassure their citizens that the European Union can be a force for good in their lives.