Others said Germany’s troubles were in many ways just a sign that the country was becoming more normal, not less. Having had only four chancellors since 1982, the country has known only a string of centrist governments that governed by consensus.

The crisis erupted seven weeks after the last election, which brought the right-wing Alternative for Germany, or AfD, into Parliament, and in some ways represented the return of politics to a country long deprived of debate and policy disagreements.

“It’s just another step in the long learning of democracy of Germany since World War II, going from a very stable proportional system to something more messy,” said Henrik Enderlein, dean of the Hertie School of Governance in Berlin.

The bigger question, he said, was whether Ms. Merkel’s pragmatic governing style had reached its limit in an era where people crave the clash of a wider spectrum of policies. “Her über-pragmatism is reaching its end,” he said. “It’s hard to see a scenario where she returns to her previous position of power.”

Ms. Merkel met in private on Monday with President Frank-Walter Steinmeier, who as head of state is charged with trying to break the deadlock in coalition talks. He could appoint a chancellor to lead a minority government or, failing that, set in motion the process for new elections.

The potential for instability in Germany would be a major blow to the European Union. Ms. Merkel has been the region’s dominant political figure of the past decade, credited with guiding the bloc through the aftermath of the 2008 financial crisis and, more recently, providing a powerful counterpoint to populists across the Continent and beyond.

Financial markets reacted calmly to the turmoil in Berlin, calculating that the German economy could power through the uncertainty. After opening lower, the DAX index of major stocks closed the day higher. The euro fell slightly.