The Dax closed on Monday at 25,389.10 points, crossing the 25,000 mark for the first time since the start of the Iran war. Hopes for a peace agreement drove the gains.
The German benchmark index rose 2.01 percent and reached its highest level since the end of February. The MDax, SDax and Euro Stoxx 50 also posted clear gains.
Market participants attributed the rise to US President Donald Trump's statement that the United States was close to a framework agreement with Iran to reopen the Strait of Hormuz. Oil prices fell amid the speculation.
Analysts such as Kyle Rodda of Capital.com and Timo Emden of Emden Research expressed skepticism and warned against excessive expectations. Trading volumes remained low due to the Memorial Day holiday in the United States.