The rights group said on Friday the number is almost triple the officially disclosed figure.
Valentina Malnikova, a representative of the respected group, told Moscow Echo radio that the figures included soldiers who died on their way to a hospital or from injuries at a later date.
These deaths are not officially registered by the Russian authorities.
The estimate suggests that, on average, nearly nine Russian soldiers have died daily since President Vladimir Putin launched the self-declared "anti-terror" campaign in October 1999.
"Unfortunately, our way of counting the dead soldiers more closely corresponds to reality," Malnikova said.
Russia rarely issues official tolls from the conflict, and when it does the figures often contradict each other.
The latest official estimate puts the Russian toll at more than 4,500 dead and the Chechen toll at about 15,000.
Chechens are fighting for an
Civilian casualties have never been officially disclosed but rights groups fear the figure could stand in the thousands.
Putin has scheduled presidential elections in the Muslim republic for 5 October as part of a peace process that has been rejected by most Chechen leaders.
Most Chechens reject Russia's attempts to make them submit to its will.
Daily guerrilla fighting rages in Chechnya despite Putin's declaration that the war has been won and that troops in the republic are there only to perform policing functions.
In the latest strike last Friday, 50 Russian servicemen and medics were killed and 78 injured when a man rammed a truck packed with explosives through the gates of a military hospital in North Ossetia.