The suicide bomber who blew himself up outside a German concert Sunday night, injuring 15, had declared allegiance to the leader of Islamic State, Bavarian Interior Minister Joachim Herrmann said.

The bomber, a 27-year-old Syrian man who was supposed to be deported, had bomb-making materials in his apartment, Mr. Herrmann said on Monday. Those materials included fuel, hydrochloric acid, alcohol-based cleaner, soldering irons, wires and pebbles.

On his phone, authorities found an Arabic-language video in which the bomber threatens an attack against Germans “in the name of Allah” and pledges allegiance to Islamic State leader Abu Bakr al-Baghdadi, Mr. Herrmann said.

“He then warns explicitly of an act of revenge against the Germans because they are obstructing Islam,” Mr. Herrmann said. “According to this video, it is beyond doubt that this attack was a terrorist attack with a perpetrator who had Islamist convictions.”

Islamic State on Monday called the bomber, a “soldier of Islamic State” in a statement on Amaq news agency, its media arm. It said the attack was in response to U.S.-led coalition attacks in its self-declared caliphate in Syria and Iraq.