Russia's most wanted Islamist has claimed last month's shooting in Moscow of a top colonel who was convicted of strangling to death an 18-year-old girl in war-torn Chechnya.

A man who identified himself as guerrilla leader Doku Umarov said in a video message posted on the rebel Kavkazcenter website on Saturday evening that he was responsible for colonel Yuri Budanov's death.

"I am addressing you today about a joyous occasion: yesterday, on June 10, Allah by his will brought us a great celebration, punishing one of the sadists, the reprobate, the killer Budanov," said Umarov.

"The same fate, the same revenge awaits the others," he added.

"Let these celebrations happen more often for Muslims."

He was shown sitting next to a heavily bearded man identified as commander of the Riyadus-Salikhiyn Brigade -- the same group that organised the 2004 school hostage crisis in Beslan that killed 334 people.

Budanov -- a tank commander who was the most senior officer convicted of war crimes in the nearly two decades of fighting in Chechnya -- was jailed in 2003 following a controversial trial of the murder of local teen Elza Kungayeva.

He was released in January 2009 after serving less than six years of his 10-year sentence and having sexual assault charges dropped despite family protests.

Budanov became a nationalist hero even before his conviction but preferred to stay out of politics and the public limelight once he was released.

The discovery of his bullet-riddled body raised immediate fears of reprisal attacks from Russian nationalists and concern that the killing was meant to further stir ethnic tensions.

Budanov's funeral was attended by Russian far right leaders such as Vladimir Zhirinovsky and accompanied by a formal three-gun salute.

Moscow police reported making a dozen arrests immediately after the slaying before closing most of the investigation to the press.

But an unnamed police source told Interfax that investigators were now studying Umarov's tape.

"We have been expecting this kind of statement for a long time because the 'Chechen version' is one of the main ones we are working with," an unnamed member of the investigative team told the news agency.

"Nevertheless, these types of terrorist statements will not alter the course of our probe," the investigator added. "We are studying all the leads."

Umarov is one of Russia's most wanted men who has claimed responsibility for most of the country's recent deadly bombings.

But regional analysts report recent defections within his ranks in the North Caucasus and note that time delays between Umarov's statements and the events they refer to suggest that he remains cut off from much of the world.