The brothers' mother, Zubeidat Tsarnaev, said Friday that she and her husband had left their home in Dagestan for another part of Russia.
Their father, Anzor Tsarnaev, had said he'd planned to travel to the United States, but that trip has been delayed indefinitely for health reasons.
The mother has said she will not return to the United States, where she is wanted on felony charges of shoplifting and destruction of property.
The family lived in Massachusetts before Zubeidat Tsarnaev jumped bail after her arrest on the charges in 2012. The parents moved to Dagestan, a semiautonomous republic in southern Russia that year.
Zubeidat Tsarnaev has denied the reality of the bombing. She believes it was fake. She said she has seen a video pushing the wild idea, and that there was no blood, that paint was used instead.
Botched hijacking thwarts plans to head to New York
Three days after the marathon attack, and hours after authorities released images of the two suspects, they spontaneously decided to go to New York's Times Square to blow up their six remaining explosives, Dzhokhar Tsarnaev told investigators.
But a botched carjacking spoiled the impromptu road trip, said Tsarnaev, whose account was outlined by New York's police commissioner.
Before forcing their way into a vehicle the night of April 18, the brothers fatally shot a campus police officer at MIT, police said.
The vehicle they subsequently hijacked, a Mercedes sport utility vehicle, ran low on fuel, and they stopped at a service station, where the vehicle's owner escaped. Shortly thereafter, police picked up the trail of the SUV and pursued it. Authorities say the men threw bombs out the vehicle's window at them. The gun battle and Tamerlan Tsarnaev's death followed.