He said wide-scale crimes had been committed during the security sweeps, which came in response to a rebel landmine which killed five Russian soldiers.
"Those who conducted the cleansing operations in Sernovodsk and Assinovskaya did so in a clumsy, lawless fashion, destroying everything and then pretending they knew nothing about it," said General Vladimir Moltensky.
He said wide-scale crimes had been committed during the security sweeps, which came in response to a rebel landmine which killed five Russian soldiers.
The general said a special operation to restore public confidence in the army would begin on Wednesday.
He said troops would have to rebuild destroyed houses and provide people with food to compensate for their actions.
Residents in the villages of Sernovodsk and Assinovskaya say troops rounded up about 1,000 men aged between 15 and 50 and beat and tortured many of them.
Human rights campaigners and a Russian parliamentary deputy say at least five people have been murdered and more than 20 are still missing.
Russian prosecutors are investigating the allegations and President Vladimir Putin's envoy, Viktor Kazntsev, has already apologised to Chechen civilian leaders over the soldiers' actions.
Russia's extraordinary self-criticism comes amid an unusually high level of Russian media coverage of the raids.
It also follows criticism from the New York-based group, Human Rights Watch, which reported on the beatings, and another human rights organisation, the European Committee for the Prevention of Torture (CPT), which was sharply critical of Russian actions in the breakaway republic.
CPT said Russia had breached its obligation to co-operate with the committee and to uncover and prosecute those responsible for human rights abuses.
CPT experts who visited the region in March this year heard "numerous credible and consistent allegations... of severe ill-treatment by federal forces", a statement from the group said.
"The CPT's delegation found a palpable climate of fear. Many people who had been ill-treated and others who knew about such offences were reluctant to file complaints to the authorities."