Up to 100 servicemen died when the huge Mi-26 helicopter, which was carrying 112 soldiers and airmen, came down near the capital, Grozny.
Chechen guerrillas have claimed that they shot it down.
Witnesses are reported to have seen an unidentified man fire the Russian-made Stinger-type rocket from the second floor of a ruined building near the site of the wrecked helicopter.
Russian President Vladimir Putin has declared Thursday a day of national mourning for the victims of the crash.
Meanwhile the Russian army has suspended all flights of Mi-26 helicopters over Chechnya for the duration of the inquiry into the crash.
The crash is Russia's worst loss in its latest 35-month campaign in the separatist republic.
