Lawyers for the family of Andrew Brown Jr, a black man killed by sheriff's deputies in North Carolina, said an independent post-mortem examination showed he died from a "kill shot" to the back of his head.
The FBI on Tuesday opened a civil rights investigation into the shooting.
Brown, 42, was struck by four bullets to his right arm before the fatal shot penetrated the rear of his skull as he tried to drive away, the lawyers told a news conference in Elizabeth City, where the shooting took place last Wednesday.
Official post-mortem examination results have yet to be released, although the death certificate indicated Brown died of a gunshot to the head.
Lawyer Ben Crump told of the fatal shot as detailed in the private post-mortem examination conducted by Brent Hall, a former medical examiner in Boone, North Carolina.
"It went into the base of the neck, bottom of the skull and got lost in his brain. That was the cause of death," Mr Crump said.
Shortly after the briefing, the FBI's Charlotte Field Office announced it had opened a civil rights investigation into the shooting, saying it would work with prosecutors in the US Department of Justice to "determine whether federal laws were violated".
Brown's death led to six nights of protests in Elizabeth City and came a day after former Minneapolis police officer Derek Chauvin was convicted of murdering George Floyd, in a trial that put a spotlight on police violence against black people.
The Brown family's lawyers called his death an "execution", saying deputies from the Pasquotank County Sheriff's Office continued firing their weapons after Brown drove his vehicle away from them.
The lawyers have also accused officials of withholding evidence after being shown only 20 seconds of footage from one police body camera on Monday.
"An innocent man was killed by law enforcement. Overkill," lawyer Harry Daniels said on Tuesday. "He wasn't fleeing. He was trying to run because he was scared for his life."
Pasquotank County Sheriff Tommy Wooten and Chief Deputy Daniel Fogg have said the deputies were trying to serve warrants on Brown from a felony drug charge, and that he had a history of resisting arrest.
They urged the public to reserve judgment until all evidence from the shooting was reviewed by the State Bureau of Investigation.
"This tragic incident was quick and over in less than 30 seconds, and body cameras are shaky and sometimes hard to decipher," Sheriff Wooten said in a video posted on social media on Monday.
"They only tell part of the story."
His office said on Friday that seven sheriff's deputies had been placed on administrative leave after the shooting.
Mr Crump said on Monday that there was evidence from at least nine cameras, including police body-cam and dash-cam videos, but that Pasquotank County Attorney Michael Cox had decided against showing more to the family.
Sheriff Wooten has said his office is seeking court approval to release the video to the public, which is a necessary step under state law.
A court hearing is scheduled for Wednesday on whether the body-cam footage can be disclosed.
Khalil Ferebee, Brown's son, said the independent examination and video evidence confirmed that his father was trying to "get away" when the officers shot him.
A family lawyer said on Monday there were seven or eight officers at the scene.
"Yesterday, I said he was executed," he said. "This autopsy report shows me that was correct."