Budanov was sentenced to 10 years in prison for killing Elza Kungayeva, 18, in Chechnya in 2000.
He walked free from an Ulyanovsk region prison Thursday after a court paroled him last month, citing the fact that he had spent more than five years in pretrial detention and had demonstrated good behavior in prison.
A lawyer for Kungayeva's family, Stanislav Markelov, said Thursday that Budanov's release was illegal and that he had filed a complaint but his appeal was rejected, Interfax reported.
Nurdi Nukhazhiyev, Chechnya's human rights ombudsman, has requested that a new criminal case be opened against Budanov, Interfax said.
The Chechen branch of the Investigative Committee said Thursday that Nukhazhiyev had provided investigators with documents from four Chechnya residents accusing Budanov of involvement in the murder and kidnapping of their relatives in 2000.
Budanov, who has always maintained that he believed Kungayeva was a rebel sniper and strangled her during an interrogation, has become a rallying figure for Russian nationalists who claim that his conviction was merely an attempt to appease the restive republic's leadership.
Chechen President Ramzan Kadyrov earlier this week decried the decision to parole Budanov. "I don't believe in the repentance of a man who committed such a crime," Kadyrov said, Interfax reported.
The decision sparked protests in Chechnya in December 2008 and the indignation of human rights organizations.
The victim's father, Visa Kungayev, told Interfax on Thursday evening that he intended to push for a new criminal probe against Budanov over the purported rape of his daughter, a charge that was dropped early in the original investigation.
He accused Budanov of securing his early release with assistance from "his influential friends," Kommersant reported. Kungayev also said he and his family feared retribution from Budanov upon his release.
Budanov was arrested in 2000, but a court concluded in 2002 that he could not be held criminally responsible because of brain injuries he had sustained in combat during federal forces' second military campaign in Chechnya.
That ruling was overturned by the Supreme Court in 2003.
Budanov's appeal for early release was his fifth, with all of his earlier requests being rejected. The Ulyanovsk court's decision to release him prompted large-scale protests last month in Grozny.
Budanov left the prison in an unknown direction and did not say where he was going or what he planned to do after his release, Interfax cited an Ulyanovsk regional prison service official as saying.
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