In one ruling, the court awarded damages to relatives of 11 civilians killed in the Grozny suburb of Novye Aldy during a February 2000 Russian military operation that killed at least 60 people.
The court also awarded damages to relatives of two civilians killed by Russian forces in the Chechen village of Gekhi in August 2000.
In June, a military court in southern Russia sentenced four soldiers to sentences of between nine and 14 years in prison for killing six civilians in Chechnya. The case was seen as a test of Moscow's willingness to acknowledge atrocities by federal troops.