Some economists and the business lobby have suggested that a nationwide minimum wage would in fact lead companies to cut jobs, particularly in eastern Germany. Almost 24 years after the Berlin Wall came down, wages in the former Communist east are still lower than in the west.

On Wednesday, the chancellor gave her first policy speech since the election and also warned of the dangers that a minimum wage could pose for jobs. Germany has an unemployment rate of 5.2 percent, according to Eurostat in Brussels, compared with a 12 percent average among the 17 members of the European Union that use the euro.

In her speech, Ms. Merkel gave little hint of any change in policy toward Europe, but said that “Europe should emerge from its crisis stronger than when it went into it,” as she said Germany had after the financial crisis of 2008 and 2009.

The election was fought largely on domestic issues, with the clearest differences between the two centrist groups emerging over the minimum wage, the definition of family in 21st-century Germany and what that means for everyone: working mothers, children of kindergarten age or gay couples seeking to adopt.

There is broad consensus that education and the creaking infrastructure of roads, railways and the Internet need attention, but there are differences over how to pay for the needed improvements. Health care, particularly for older citizens, and pensions are other areas of differences which will now be pored over in detail by both camps.