General Alexander Savenkov told journalists in Moscow on Tuesday that "the decision to render a second acquittal in this case has nothing to do with justice".
A jury at the military court in the southern Russian town of Rostov-on-Don cleared the four officers from the elite Main Intelligence Directorate (GRU) forces of murder on 19 May.
It was the second such trial, the first acquittal having been overturned on a technicality.
The officers admitted to their roles in the killing in 2002 of six Chechens, including a village school teacher and a pregnant mother of seven. However, the jury accepted their defence that they were simply acting under orders and not responsible.
"I am absolutely convinced that what they did should be punished by the law. It is clear that we will do everything so that justice wins," Savenkov said.
The trials were among only a handful of attempts in the past decade to bring Russia's military to book for what are widely said to be mass human rights violations in Chechnya.