"They have heard reports that my lawyer was killed in central Moscow in broad daylight and have taken us under protection," he said in a telephone conversation.
The family's daughter, Elsa, was murdered in Chechnya in 2000 by a Russian military officer and their lawyer, Stanislav Markelov, was shot dead in downtown Moscow on Monday.
Kungayev said that he was summoned to a police station on Tuesday morning to discuss Markelov's murder and the Kungayevs' safety, after which the police have been watching their house and movements.
Kungayev said his family was forced to move from Russia to Norway after receiving threats over the Yury Budanov case.
Budanov, who commanded a tank regiment during the second military campaign in Chechnya, 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 earlier this month.
Markelov handled the family's appeal against Budanov's early release, claiming he "was still threatening the Kungayev family," but a court rejected their plea last Thursday just hours after the former officer was released.
Kungayev said earlier on Tuesday he would hire a new lawyer to appeal the killer's early release. "Definitely, I will pursue the case to its end," Kungayev said in a telephone interview.
Kungayev said on Monday that he had no doubts that the shooting of Markelov was directly connected with the Budanov case.
"We are all shocked. We did not expect this. I am sure that he was killed for his professional activities, particularly for the Budanov case," he said.
Markelov was shot in the back of the head while walking along a Moscow street shortly after finishing a news conference devoted to Budanov's release. Novaya Gazeta journalist Anastasia Baburova, 25, was wounded in the shooting and died in hospital later on Monday.
Budanov has flatly denied any involvement in the lawyer's death.
"This is a dirty provocation that has nothing to do with me," Budanov was quoted as saying by popular Russian tabloid Komsomolskaya Pravda.
Besides representing Kungayeva's family, Markelov had started an independent investigation into an attack on Mikhail Beketov, editor-in-chief of the local Khimki Pravda newspaper.
Beketov, who fought a campaign against the construction of a toll expressway through a forest in Khimki, a city northwest of Moscow, was found unconscious in the street on November 13 after being badly beaten near his home.