Further signals from the US Federal Reserve (Fed) towards a more moderate interest rate policy gave the Dax a boost on Thursday.
However, retail sales in Germany in October put a damper on sales, which unexpectedly fell sharply in view of the high inflation.
The leading German index rose by more than one percent at the start of trading.
Later it was still an increase of 0.6 percent to 14,484 points.
The M-Dax of medium-sized stocks increased significantly by 1.6 percent to 26,012 points.
The Euro Stoxx 50, the leading index in the euro zone, gained 0.5 percent to 3984 points.
A speech by US Federal Reserve Chairman Jerome Powell caused the US stock exchanges to turn positive on Wednesday and triggered a price rally on Wall Street.
Powell lulled financial markets into a less aggressive stance on interest rates ahead of the last Fed meeting of the year.
"As early as December" could be the time to slow down rate hikes, the Federal Reserve chairman said.
The probability of a rate hike of 0.50 percentage points for the December 14 meeting is now estimated on the financial markets at 75 percent.
At the beginning of November, the Fed raised the key interest rate for the fourth time in a row by 0.75 percentage points to the new range of 3.75 and 4 percent.
The Dow Jones index of standard values then closed 2.2 percent higher on Wednesday at 34,589 points.
The tech-heavy Nasdaq advanced 4.4 percent to 11,468 points.
The broad S&P 500 gained 3.1 percent to 4080 points.
Technology stocks particularly in demand
The US economic data published on Wednesday were mixed.
On the one hand, gross domestic product from June to September increased by 2.9 percent on an annualized basis.
Experts had expected an increase of 2.7 percent.
On the other hand, according to a survey, US companies created significantly fewer jobs in November than expected.
The bottom line was that 127,000 jobs were created, well below the average analyst forecast of an increase of 200,000.
Technology stocks were among the winners following the Powell speech.
The papers from Microsoft, Netflix and the graphics card manufacturer Nvidia rose by up to 8.7 percent.
According to experts, rising inflation and higher interest rates will devalue the future profits of these high-growth companies.
At the same time, the brightening prospects in China caused oil prices to rise.
US light oil WTI rose 2.7 percent to $80.30 a barrel (159 liters).
Prices were also supported by falling crude stocks.
Recently, speculation about the future production policy of the oil association Opec+ had caused sharp price fluctuations, but insiders say his decision to hold the meeting online on December 4 indicates a low probability of a change in policy.
In terms of individual values, the shares of the electric car manufacturer Tesla rose by 7.7 percent after strong sales figures on the Chinese market.
Thanks to lower prices and other incentives, the American group sold almost twice as many vehicles in the People's Republic in November as in the same month last year.
Boeing's shares also gained more than two percent.
According to insiders, the aircraft manufacturer can hope for a compromise with the legislator when it comes to the endangered approval of two variants of its medium-haul jet 737 Max.