"Lawyer Stanislav Markelov was killed near building No. 1 on Prechistenka Street. Documents bearing his name were found on the body," Anatoly Bagmet, an official with the Prosecutor General's office, told journalists.
Budanov, who commanded a tank regiment during the second military campaign in Chechnya, was convicted in the summer of 2003 of strangling an 18-year-old Chechen woman three years earlier and was sentenced to 10 years in jail. He was paroled earlier this month.
Elsa Kungayeva's family had appealed against Budanov's early release, but a court rejected their plea last Thursday just hours after the former officer was released.
A source in the law enforcement bodies said earlier that Markelov was shot dead with a gun fitted with a silencer at around 2 p.m. Moscow time (11:00 GMT) near the Kropotkinskaya metro station in Moscow downtown.
"An assailant ran from behind to Markelov and a woman escorting him, Anastasia Baburova, and shot him in the back of the head from point-blank range. The woman tried to get hold of the suspect, but he shot her too," the source said.
Police said earlier that one man was killed and two more seriously wounded after an unknown suspect opened fire on them.