The 28-year-old first lieutenant, who had falsely registered as a Syrian refugee, was arrested in Bavaria last week. A suspected accomplice, a 24-year-old student, was also detained after being found in possession of explosives.
Von der Leyen told ZDF television on Sunday night that the arrested officer had written a paper for his Master's at a military academy that was filled with "primitive racial ideas" that drew initial scrutiny from superiors but were then "whitewashed" in an "ill-advised esprit de corps".
"People look the other way and it starts to ferment until there's a scandal," she said.
"The Bundeswehr [army] has an attitude problem and it evidently has weak leadership at different levels."
German army officer pretended to be Syrian refugee, planned terrorist attack
On Monday she sent a follow-up letter to all members of the armed forces, saying she had asked the army's inspector general to examine any extremist or racist tendencies and why such problems had not been properly and fully tackled.
She asked the soldiers for their support and understanding for her efforts to dig into this and other recent cases of crimes and racism involving soldiers.
The chairman of the Bundeswehrverband, a lobby group that represents members of the armed forces, criticized von der Leyen's 'weak leadership' remarks.
"Her comments leave us bewildered and outraged," André Wuestner told the Passauer Neue Presse newspaper.
"If the minister is truly serious about that, then she's massively damaging the Bundeswehr. To say all 250,000 in the Bundeswehr have an attitude problem affects us all."
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The arrested soldier had previously been detained in late January by Austrian authorities on suspicion of having stashed a gun in a bathroom at Vienna's Schwechat airport. Investigators later discovered he had used a fake identity to register as a Syrian refugee, even though he spoke no Arabic.
The bizarre case touches on two sensitive issues in Germany: the right-wing extremism that occasionally plagues the country, and the turmoil surrounding the influx of more than a million migrants, many from the war in Syria, since 2015.
"It's not in order that the superiors didn't grasp what was going on and didn't understand their responsibility," said von der Leyen.
"Evidently, the early-warning mechanisms the forces have in place didn't work, and that has to be investigated," she said.
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