Todashev's parents filed a "notice of claim" Monday, saying they plan to seek $30 million in a wrongful death lawsuit.
The claim argues the FBI has given "no viable justification" to account for shooting and killing Todashev during a 2013 interrogation in Todashev's apartment in Orlando, Florida.
The interrogation occurred about a month after the Boston Marathon bombings and centered around another crime linked to bombing suspect Tsarnaev: a 2011 triple homicide in Waltham, Massachusetts.
Todashev admitted to his direct role in slashing three people's throats in Waltham and said Tsarnaev was involved as well, a federal law enforcement official told CNN in 2013. It was during that interview that Todashev was shot dead.
The Council on American Islamic Relations Florida filed the notice of the Todashev family's intention to sue on Monday.
"We are seeking answers and justice for someone who was shot seven times by an FBI agent in his own home after hours of interrogation," said Ali Kurnaz, a spokesman for the civil rights group.
Many things that happened that day don't add up, Kurnaz said.
"Todashev was unarmed with any gun, knife, explosive or other deadly weapon," the notice says. "Todashev did not pose a threat of serious bodily harm."
The FBI did not immediately respond to a request for comment.
One law enforcement official said Todashev attacked the FBI agent with a broom handle, gashing his head before the agent opened fire. At the time, the official stressed that the shooting was justified and done in self-defense because the agent felt threatened.
A U.S. government official briefed on the investigation rebuffed the idea that Todashev wasn't a threat -- noting, for instance, that he could have taken the agent's gun.
"He was armed. Maybe it wasn't a weapon, but he had a long object," the official said. And because of Todashev's martial arts expertise, "he was a weapon himself."
"My son was definitely unarmed, because he never had a gun," father Abdulbaki Todashev told CNN in 2013
. "He couldn't attack them or fight them; he couldn't do anything because even two men could easily handle him."
The elder Todashev suggested his son may have been provoked. "If you question someone for eight hours, you can provoke him into anything," he said.
"(Todashev) went down, but he was not incapacitated. He came up again in an aggressive manner, and the officer then fired the second volley of three or four shots. Which at that point essentially incapacitated Mr. Todashev," Ashton said.
"It would seem almost superhuman, but everything that we have learned in the investigation would show an individual who has a great deal of tolerance of pain and would more or less fight beyond it.
"It seemed to me that if the goal was to get away, he could have gone out that back door and gotten away instead of going towards the officers."