The Strasbourg-based court was on Thursday ruling on claims by six Chechens who blamed Moscow for the deaths of relatives during attacks and bombings by the Russian military in 1999 and 2000.
The court ordered Moscow to pay a total of 135,710 euros ($179,900) in damages to the six claimants.
The panel of judges, among them one Russian, were unanimous in condemning Russia for breaching the European Convention of Human Rights article on the right to life.
The court also said Moscow breached the plaintiffs' right to a full hearing.
It said in two cases, Moscow had also violated the ban on torture and inhumane or degrading treatment and, in the case of one person, breached a clause on the protection of property.
Two of the six Chechens alleged they were tortured and family members were killed by the Russian military in Grozny, the Chechen regional capital.
Two of the six Chechens alleged
that they were tortured
The others complained of the shelling of civilians in late 1999 and early 2000, during a flare-up in the conflict between Russian forces and separatists which has raged on and off since 1994.
Russia can request the case be referred to the court's grand chamber for a final judgement within the next three months.
Chechen separatists meanwhile announced on Tuesday that they had ended a unilateral ceasefire they called at the start of the month and said they could soon return to offensive operations.
But pro-Moscow officials, who have tightened security in the mountainous region, said the truce had had no effect on the level of activity there.
Hundreds of thousands of civilians are believed to have been killed and some 20,000 soldiers have died since Russia first sent in troops to crush separatist rebels in 1994.
The six cases were the first of about 120 concerning the Chechen conflict submitted to the court.