Police said that a.38-calibre pistol was discovered at McDole's side after police shot him dead, but McDole's family insist that he was not carrying a gun.
McDole, 28, had been confined to a wheelchair after he was shot in the back ten years ago, which paralyzed him from the waist down.
Wilmington, Delaware police chief Bobby Cummings said that McDole was shot because he did not obey police commands to show his hands and put his weapon down.
At the news briefing, Jeremy McDole's mother Phyllis McDole called the shooting "unjust."
"He was in a wheelchair, paralyzed from the waist down. There's video showing that he didn't pull a weapon… I need answers," said Phyllis McDole.
"He had a book bag, but I never saw a gun," said the victim's uncle Eugene Smith shortly after the shooting on Wednesday.
"It was an execution. That's what it was. I don't care if he was black, white, whatever."
Cellphone footage of the shooting was posted online. Some viewers may find this video too graphic.
"I have great confidence in the investigation," said Markell, who also met with McDole's relatives.
Richard Smith, head of the Delaware chapter of the NAACP, a national civil rights organization, called for an investigation which would not involve "cops investigating cops," and instead be carried out by a special prosecutor.
"We cannot continue having all our folks being shot and nobody held accountable," said Smith.
