German authorities said they had found a hand-painted IS flag among the belongings of the asylum seeker, who seriously injured four members of a family of tourists from Hong Kong in his rampage. The teenage assailant was killed as he tried to flee.
"The perpetrator of the stabbing attack in Germany was one of the fighters of the Islamic State," the IS-linked Amaq news agency said.
The assault on a regional train near the southern city of Wuerzburg late Monday left two of the victims critically hurt, said Joachim Herrmann, the interior minister of Bavaria state.
Germany has thus far escaped the kind of large-scale jihadist attack seen in the southern French city of Nice last week, in which 31-year-old Mohamed Lahouaiej Bouhlel used a truck to mow down 84 people. That attack was also claimed by IS.
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The terrifying assault in Bavaria is likely to revive a heated national debate about integrating migrants and refugees after a record influx last year.
The assailant had arrived as an unaccompanied minor in Germany about two years ago and had been staying with a foster family in the region for the last two weeks, Herrmann said.
However, he stressed that the investigation was ongoing and that the teenager appeared to have acted alone.
"We must determine what the motive was and to what extent he really belonged to the Islamist scene or self-radicalised very recently," Herrmann said, adding that the assailant had no criminal record in Germany.
The assault happened around 9:15 pm (local time) on the train which runs between the town of Treuchtlingen and Wuerzburg in Bavaria.
The man, who declined to give his name, said he saw people crawl from the carriage and ask for a first-aid kit as other victims lay on the floor inside.
"The perpetrator was able to leave the train, police left in pursuit and as part of this pursuit, they shot the attacker and killed him," a police spokesman said.