The man, identified as 27-year-old Maximilian T, was detained in Kehl, a town in south-western Germany located on the river Rhine on Tuesday (9 May).
Arrested men "were ready to kill for their cause", according to an investigator.
Officials would also revamp the "Traditionserlass", a policy last updated in 1982, which provides guidance for how troops should treat the legacy of the German military, which also coordinated a failed attempt to assassinate Nazi leader Adolf Hitler in 1944.
A second soldier has been arrested for allegedly planning a "false flag" terror attack to be blamed on refugees in Germany amid fears of a wider neo-Nazi network within the army.
Germany's embattled defense minister has pledged to reform the country's armed forces following the arrest of two soldiers alleged to have plotted a terrorist attack they tried to blame on refugees.
Numerous attacks have been induced by a historic flow into Germany of refugees, some of them recruited by terror groups to carry out attacks on crowded places in large German cities.
As well as the loaded 7.65mm pistol stashed in a toilet at Vienna International Airport, around 1,000 rounds of ammunition were found at Mathias F's home in Offenbach - mostly stolen from the German army.
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Maximilian T and Franco A were stationed at the same Franco-German base near Strasbourg. Potential targets that were on the list include former German President Joachim Gauck and left-wing justice minister Heiko Maas (SPD).
German police Tuesday arrested two suspected Syrian jihadists, one of them an alleged member of the Islamic State group accused of slitting the throat of a regime soldier, prosecutors said. A master's thesis, which clearly included racist, extremist views ... did not have any consequences for this soldier.
The defence minister, Ursula von der Leyen, has come under fire for her handling of the case after attacking "weak leadership" following the discovery of 275 suspected right-wing extremists within Germany's military.
Amid the widening scandal, parliament's defense committee held an extraordinary meeting with Von der Leyen, which was closed to the public.
The Bundeswehr is now conducting searches of army barracks across the country in search of Nazi-era memorabilia as part of the probe into far-right sympathizers.
"All these happened during the term of the minister".
The initial warm reaction the asylum seekers from Syria, Iraq, and Afghanistan received upon arrival in Germany has soured, with several high-profile incidents leading to an anti-Muslim backlash, rising nationalism, and hate crimes.