But the latest decline in joblessness  also raised fears among some economists that the pace of German growth  could become unsustainable.

On a seasonally adjusted basis, unemployment fell below three million people for the first time since 1992, as Germany continued to benefit from strong exports of autos and other products. The jobless rate, 7.1 percent,  was unchanged from March, but down  from 7.8 percent last April. 

“The order books are full, capacity usage is high and help-wanted ads are  rising every month,” Rainer Brüderle,  the German economics minister, said in  a statement. The news came a day after estimates that inflation in Germany rose to an annual rate of 2.6 percent this month, well above the European Central Bank’s goal of 2 percent. The drop in unemployment also highlighted the divergence between booming Germany and slow growth in most of the rest of Europe.

 The average unemployment rate in  the euro zone last month was 9.9 percent, and Ireland and  Spain have jobless rates more than  twice as high as Germany’s.

Monetary policy in the euro zone is probably too loose for Germany, some economists say. Excessively low interest rates can lead to asset bubbles  and inflation, and set the economy up  for a painful retreat. “I see a long-term risk that Germany could overheat,” said Jörg Krämer, the chief economist at Commerzbank in Frankfurt. “It’s an ugly situation for the E.C.B.”

Just this month, the central bank raised its official rate to 1.25 percent, the first increase since 2008. The appropriate rate for Germany would be closer to 3 percent, Mr. Krämer said.

The euro has risen steadily against the dollar since January because of expectations that the central bank will continue to raise rates, in part because of the need to slow the German economy. On Thursday the euro rose to just short of $1.49, its highest level since the end of 2009, before falling back slightly.

Higher interest rates tend to raise the value of the euro by making it more attractive for investors to own euro assets.

As unemployment in Germany falls, companies may need to pay more to attract workers, which could further fuel inflation. In the prosperous southern states of Bavaria and Baden-Württemberg, home to the carmakers BMW and Daimler, jobless rates were only about 4 percent in April. Companies report problems finding skilled workers.

 “Price and wage inflation should remain moderate,” economists in London  for Nomura wrote in a note, but added,  “German trade unions have become  more vocal in their wage demands.”

Still, various factors could limit wage inflation. Mr. Krämer noted that most union wage contracts did not expire until next year. In addition, beginning in May companies will be allowed to freely hire people from European Union countries like Poland or the Czech Republic. And jobless rates in much of eastern Germany remain above 10 percent.

However, Mr. Krämer said, “The time of ultralow wage increases in Germany is definitely over.”

Jean-Claude Trichet, the European Central Bank president, has consistently denied that there is any inherent problem in fashioning a monetary policy that fits fast-growing countries like Germany and poorer members of the euro zone.

Speaking to reporters earlier this month, Mr. Trichet said Germany’s return to growth after years of stagnation was good for its neighbors.

“We had an episode of a return to competitiveness, of hard work, and now we see the result of this hard work,” Mr. Trichet said in Frankfurt on April 7. “It is good for Germany and good for the euro area as a whole.”

Central bank data published this week  showed that negative pressures on the euro area continue even as  inflation quickens. Banks remain reluctant to lend because some are having  trouble raising capital, while demand for  home loans is decreasing, according to a bank survey published Wednesday.

 The information could reassure the  central bankers that they do not need to  be unduly hasty to raise rates.

While seasonally adjusted unemployment fell below three million, the absolute number of jobless people remained above that milestone, at 3.08 million. Economists consider the seasonally adjusted number a more reliable indicator of the strength of the economy.

In any event, the absolute number of jobless people will probably fall below three million next month, economists said.

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