"What was recently revealed in a report broadcast on Channel Two is that they asked soldiers questions which were unrelated to morality and the character of their activity," his office quoted him as saying in Hebrew.
He said that in collecting testimony on their military service the ex-soldiers were quizzed on "what are in effect operational secrets."
"If this material is distributed externally it is treason," he said. "Also if they only keep it to themselves, who guards this material?"
The NGO, Breaking the Silence, provides a platform for military veterans to describe what they say are disturbing aspects of their service in the 2014 war in the Gaza Strip and in operations in the Israeli-occupied West Bank.
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Israeli TV station Channel Two aired a report Thursday that it said showed the activists collecting testimony from ex-soldiers and asking them about military equipment and operational methods.
The next day Yaalon ordered the army to investigate alleged security breaches.
Yuli Novak, president of Breaking the Silence, has denied any improper behaviour by her group, saying that in order to verify soldiers' accounts researchers must ask questions about dates, locations and the identity of units allegedly involved.