
A spokeswoman said police were checking witness statements that the man shouted "Allahu Akbar" ('God is Greatest' in Arabic) during the attack, adding that the perpetrator had been arrested.
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Germany's ARD broadcaster reported that one man had died from his injuries. Police could not confirm this.
The attack took place in the S-Bahn commuter train station at Grafing, a town about 32 km (20 miles) southeast of the Bavarian capital in southern Germany. Germany, which is playing a supporting role in the fight against Islamic State, has not suffered a major attack by extremist militants on the scale of those that have hit neighbouring France and Belgium.
However, German security services are on alert and ministers have repeatedly warned of a possible attack. Over 800 home-grown radicals have left Germany to join religious extremist groups in Syria and Iraq and about 260 have returned.
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Germany has also been a transit country for militants who carried out attacks in Belgium this year and Paris last year. There are concerns that some of the 1 million migrants who arrived in the country last year have slipped off officials' radar.
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