Speaking to reporters in Makhachkala, the capital of Russia's republic of Daghestan where the family lives, Anzor Tsarnaev and Zubeidat Tsarnaeva told reporters that their sons were set up by the FBI, calling it a "spectacle."
Tamerlan died after a shoot-out with police on April 19.
Dzhokhar was captured less than a day later, after a massive manhunt. He is hospitalized with injuries and has been charged with terrorism-related offenses.
Anzor Tsarnaev said he is preparing to travel to the United States in order to understand what happened.
"I'm getting ready to travel to the United States," Anzor Tsarnaev said. "I want to see my son [Dzhokhar] and bury my older [son Tamerlan]. I have no bad intentions. I'm not going to blow anyone up. I don't want to do anything [like that]. Do you understand? I have no hard feelings about anyone. I want to find out of the truth."
U.S. officials have said the federal government had added the name of Tamerlan Tsarnaev to a terrorist database 18 months before the Boston bombings.
The officials, who spoke on condition of anonimity, said the CIA added Tsarnaev to the database after Russian intelligence officials contacted their U.S. counterparts in September 2011 about their concerns over Tsarnaev.
The FBI had separately investigated Tamerlan Tsarnaev but had found no evidence of a threat.
Anzor Tsarnaev confirmed that during a stay in Makhachkala last year, Tamerlan visited a mosque linked to extremists. But he downplayed its significance, saying he did not think it influenced his son.
An emotional Zubeidat Tsarnaeva said she regretted that the family emigrated to the United States.
"I would prefer not to live in America now. Why did I even go there? Why? I thought America was going to protect us, our kids, that it was going to be safe, for whatever reason. But it happened. America took my kids away from me."
The April 15 Boston bombings killed three people and injured more than 260.