“I think it’s irresponsible for tens of thousands to gather in close proximity” in countries where the “highly contagious” Delta variant is spreading, Seehofer told Germany’s Augsburger Allgemeine newspaper.
The appeal comes just hours before a last-16 clash between England and longtime rivals Germany at London’s Wembley stadium.
UEFA and the British authorities have said some 45,000 supporters will be allowed to attend the game, equivalent to 50 percent of capacity.
Attendance will be increased to 75 percent of capacity, or more than 60,000 fans, for the semi-finals and final at Wembley, in what will be the largest crowds at a sports event in Britain since the start of the pandemic.
In Germany, where Munich’s Allianz Arena has hosted several Euro 2020 matches, the capacity cap has been set at a strict 20 percent — or around 14,000 spectators.
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Seehofer said the 20-percent rule could serve as “a benchmark” to other Euro 2020 venues as well.
Britain is experiencing a surge in new coronavirus cases blamed on the Delta variant that was first detected in India.
Germany has designated Britain as a virus variant risk area, meaning only German nationals or residents are allowed to enter from the UK, barring a few exceptions.
All UK arrivals, including vaccinated people, have to quarantine for 14 days once in Germany.
Strict travel curbs imposed by both countries are expected to dissuade many German fans from making the trip to England.
Chancellor Angela Merkel has in recent days repeatedly expressed concern about the Euro championship fuelling the spread of the Delta variant on the continent.
She has also criticised a lack of European-wide coordination on entry restrictions for travellers from risk areas.
In Germany, the Delta strain now accounts for around half of all new coronavirus cases, the head of the country’s Robert Koch Institute for infectious diseases told a meeting attended by Health Minister Jens Spahn on Monday.