Tamerlan and Dzhokhar Tsarnaev, spoke to reporters at a news conference in the Russian region of Dagestan where they were living when the Boston marathon bombings took place.
The father, Anzor, calmly revealed plans to travel to the United States in the next days. But their mother Zubeidat, in a hugely emotional intervention, accused the US security services of needlessly killing her eldest son.
Tamerlan, 26, was killed in a chaotic shootout while Dzhokhar, 19, was gravely wounded during his capture by the US authorities.
Tamerlan was "killed, cruelly killed. I want to scream to the whole world, what did you do? He was alive!" Zubeidat, dressed in an Islamic headscarf, said in sometimes incoherent comments.
"He was alive! Why did they need to kill him? Why? They got him alive," she said speaking in English and standing up as her husband remained seated.
Zubeidat reaffirmed her belief that her sons were innocent of the Boston bombings. "I know one thing, that my children did not do this. There is a lot that is not comprehensible."
She also expressed worry over the injuries to Dzhokhar that he received during his capture. "He has a really bad wound on his neck. He is getting better but he is still weak."
Zubeidat and Anzor were speaking after they met investigators from the US FBI in Dagestan earlier this week in a trip organised by the US embassy in cooperation with the Russian authorities.
Anzor, wearing dark sunglasses and unlike his wife speaking mainly in Russian, said he planned to go to the United States.
"I plan to go to the United States to clear everything up. I am not looking for revenge or to offend. Let the special services sort it out," Anzor told reporters.
Anzor Tsarnaev said he expected to leave for the United States later today or tomorrow. He said Zubeidat had not decided whether to accompany him, apparently due to shoplifting charges against her dating from 2012.
"I want to see my youngest son and bury my eldest," he said.
Zubeidat said she wanted Tamerlan's body to be brought from the United States for burial at home but was not sure how this could be carried out.