The jobless rate remained stable at 7.6 percent of the workforce, the Federal Labour Agency said.
"The clear rebound of the German economy continues to translate positively onto the jobs market," the agency said in a statement.
The fall from an unadjusted figure of 3.192 million, the figure used as a public reference, meant the unadjusted jobless rate was unchanged from July as Europe's biggest economy powers out of its worst post-war recession.
The adjusted rate used by economists was also 7.6 percent in August, but the corresponding number of unemployed declined by 17,000 people, the Labour Agency said.
That was slightly below a forecast decline of 20,000 compiled by Dow Jones Newswires, but nonetheless showed continued improvement as firms rehire to meet stronger foreign and domestic demand.
It was the 14th monthly decline in a row and left the unemployment rate at close to a two-year low point, Capital Economics senior European economist Jennifer McKeown noted.
"While unemployment is still rising elsewhere in the eurozone, the German labour market has been particularly resilient, thanks initially to the Government's 'Kurzarbeit' subsidy scheme, but perhaps now reflecting the underlying economic recovery," McKeown said.
The German government had subsidised shorter working hours to help companies make it though the global economic downturn, but most companies have now put staff back on full-time hours.
Germany posted record quarterly growth in the second quarter of 2010 thanks to strong exports and a pick-up in domestic consumption underpinned by improving job prospects.
German Economy Minister said in July that the number of unemployed could soon fall below three million.
"The impressive performance of the labour market can only become a real success story if it eventually leads to a pick-up in private consumption," ING senior economist Carsten Brzeski said. "All ingredients are in place for this to happen now."