FRANKFURT (dpa-AFX) - Renewed hopes for peace in the Middle East provided fresh upward momentum for the German stock market on Tuesday. High oil prices retreated significantly.

The German benchmark Dax reclaimed the 24,000-point threshold, closing up 1.27 percent at 24,044.22 points. The MDax, which tracks mid-cap companies, gained 0.94 percent to reach 30,534.94 points. Similar trends were observed across Europe and in the United States.

Following a day of heightened tensions and mutual threats despite a ceasefire and unsuccessful weekend talks between the U.S. and Iran, new discussions were described as showing "significant progress." U.S. Vice President JD Vance spoke of these developments, adding that the ball is now in Tehran's court to make concessions on the most critical issue for the U.S.: the Iranian nuclear program.

Consequently, the possibility of ending military hostilities remains on the table. A peace agreement would also reopen the Strait of Hormuz, a vital shipping route for the global economy, according to portfolio manager Thomas Altmann of asset manager QC Partners. This could trigger a gradual normalization for the global economy.

Furthermore, the Lebanese government and Israel are set to begin direct talks for the first time in decades. According to Prime Minister Benjamin Netanyahu, Israel is seeking a permanent peace agreement and is demanding the disarmament of the Lebanese Hezbollah militia, an ally of Iran.

In Europe, the Eurozone's blue-chip EuroStoxx 50 index rose by 1.35 percent to 5,984.51 points, while gains were also recorded in London and Zurich. In the U.S., major indices were also trading higher at the time of the European market close. The price of a barrel of Brent crude oil slipped further below 100 U.S. dollars.

Within the Dax, Deutsche Bank shares led the pack with a 3.8 percent gain, while Commerzbank rose by 2.5 percent. U.S. banks JPMorgan, Citigroup, and Wells Fargo had reported first-quarter profits that exceeded expectations.

Nordex shares suffered from profit-taking following the release of order figures and a downgrade by MWB Research on valuation grounds. The wind turbine manufacturer's stock fell by 0.9 percent, though it had reached a record high only last week.

Aixtron shares continued their descent, falling another 4.2 percent after investment bank Oddo BHF withdrew its positive investment recommendation. Analyst Martin Marandon-Carlhian noted that a very strong business performance through 2027 is already priced in.

Nemetschek lost 3.4 percent. The software provider specializing in the construction industry announced the acquisition of the U.S. company Heavy Construction Systems Specialists (HCSS). While the transaction makes strategic sense, expert Charles Brennan from Jefferies judged that it comes at the expense of valuation and increased complexity.

Heidelberger Druck stood out in the small-cap SDax index with a price surge of nearly 19 percent. Speculation regarding an entry into the defense business, which had surfaced in March, was revived on Tuesday by a report in "Wirtschaftswoche" and a visit by the Minister President of Brandenburg to the Brandenburg an der Havel site. As is known, the printing press manufacturer is building a new pillar in drone defense alongside its core business and its current offering of EV charging boxes. Traders also pointed to short covering as the price momentum accelerated throughout the day. Short sellers come under pressure to close their positions through purchases when prices rise, thereby amplifying the rally.

Steel stocks benefited from the EU tightening its import rules to protect European industry. Salzgitter and Thyssenkrupp recorded gains of 5.2 percent and 3.3 percent, respectively, continuing the recovery rally that began in late March./ck/he

--- By Claudia Müller, dpa-AFX ---