Budanov, who commanded a tank regiment during the second Chechen war, was convicted in the summer of 2003 of strangling 18-year-old Elsa Kungayeva three years earlier and was sentenced to 10 years in jail. He was paroled last month.
A spokesman for the investigation committee said on Tuesday that in 2000 three residents of Chechnya's Shatoi district were abducted and later discovered dead near the village of Tangi-Chu. A criminal case was launched, but later closed as there were no suspects.
However, the spokesman said that on January 22, Nurdi Nukhazhiyev, a human rights representative and several residents of the Shatoi district had filed a document stating that Budanov was involved in the abduction and murder of the three people.
"The document stated that Budanov himself stopped the car containing the victims and took them away and their bodies were later discovered," the spokesman said, adding that the relatives of the people killed had identified Budanov from televised reports and from photographs in the press.
On January 19, lawyer Stanislav Markelov was shot dead in the center of Moscow after attending a press conference where he had protested against Budanov's release. The journalist with him, Novaya Gazeta employee Anastasia Baburova, was also killed by the unknown gunman.