Interfax news agency quoted Ramzan Kadyrov, Chechnya's prime minister, as saying: "Almost all illegal armed groups have been destroyed. Their leaders have either been eliminated or sentenced."
But Chechen separatists in exile disagreed.
Kavkaz Center, the separatists' information agency in exile, told Reuters in an email: "The rebels paraded on television were not fighters but their relatives, Chechens already in prison or separatists who gave up the struggle years ago.

"Not one mujahid has surrendered. All statements by the Russian side on the surrender of mujahidin are propaganda which bear no relation to reality."
Despite this defiance, the Chechen separatist movement seems to be at its lowest ebb for several years.
Crushing the rebellion is a matter of personal pride for Vladimir Putin, the Russian president. As acting head of state in 1999, he ordered Russian soldiers back into Chechnya, ending a period of self-rule.
After several years of fighting, Russian forces and their local allies have stopped the rebels from operating openly.
'New generation'
Aslan Maskhadov, the separatists' president, and Shamil Basayev, a commander and Russia's most wanted man, have both been killed.
But it was unclear if the Russian security operations and the amnesty had broken the rebels' ability to carry on fighting.
Alexei Malashenko, an analyst at the Carnegie centre in Moscow, said: "The main point is that we don't really know how many rebels are in the mountains.

"And [we have] no real information on the 'new generation' not only in Chechnya but also in the neighbouring states where there are signs of a new wave of disenchanted men."
On Grozny's tattered streets, war weary residents told Reuters they too were sceptical of the latest amnesty.
Zara Estamulova said: "I don't believe the amnesty, it's all stage-managed."
The amnesty has boosted the authority of Kadyrov, the pro-Moscow Chechen prime minister who also heads the region's most powerful militia force.
Analysts think the Kremlin is grooming the 30-year-old to take over as Chechnya's president.
Rebels handed over their weapons not to the Russians but to Kadyrov, himself a former rebel, in televised ceremonies at his home 30 km outside Grozny.
"It's about Kadyrov and his grand political line. It's a private amnesty agreed with Kadyrov, all the rebels now deal personally with him," said Alexei Malashenko.