Germany's top general on Thursday said it was unclear if the officer arrested last week on suspicion of planning a racially motivated attack was part of a broader network.
"We don't know that at this point. ... We are trying to examine the environment around the suspect," General Volker Wieker, inspector general of the German Bundeswehr, told the broadcaster ARD.
German media reports have said officials are looking into a possible network of five people around the 28-year-old lieutenant, identified only as Franco A.
Wieker met Defense Minister Ursula von der Leyen in Berlin on Thursday, along with 100 top generals and admirals, to discuss what she has described as "weak leadership" in the military.
Von der Leyen on Wednesday visited the barracks in the French town of Illkirch where Franco A. was serving in the German-French Brigade, set up in 2010 as a showcase of cross-border cooperation.
Von der Leyen had ordered an investigation into why the suspect's superiors had failed to report to military intelligence concerns voiced about the content of a master's thesis he had submitted during his time at a French military academy, ministry sources said.
Under German military rules, any report of extremism among soldiers must be investigated by military intelligence, the sources said, and the failure to do so in this case was a breach of civil service rules.
Wieker said the investigation was being led by the Federal Criminal Office and federal prosecutors, but military officials were assisting.
Wieker has this year begun a series of structural reforms after a sexual abuse and hazing scandal rocked the armed forces' special operations training center in southern Germany.
Von der Leyen last month fired the general in charge of training for failing to crack down on the problems at the site.