Edwards, whose death was ruled a homicide, was riding in a vehicle with other teenagers, including his older brother.
According to NBC News, police say that Oliver "violated several departmental policies", and that those specific policies can not be discussed as there is potential for him to repeal the termination.
The Texas cop who shot and killed a black high school freshman has been fired.
Balch Springs police officers have been instructed not to discuss the ongoing criminal investigation into the shooting death of Jordan Edwards.
Fatal police shootings of African-Americans have prompted criticism from victims' families over delayed action, and in some cases mass protests.
A family statement released Tuesday night called for disciplinary action against other officers who "extended this nightmare for those children".
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Initially, it was reported that an officer fired on the auto Jordan Edwards was riding in because it was reversing in an "aggressive manner" toward a police vehicle. Haber previously said the department was getting threats on social media in response to the shooting. "In a rush to get the information out, to be transparent", he said.
Crockett said Tuesday that she was optimistic that Oliver would eventually be indicted.
"Attorney Cindy Stormer, a former prosecutor who is representing Oliver, asked the public to be patient while the six-year veteran of the department is investigated".
"Our family is working hard to deal with both the loss of our beloved Jordan and the lingering trauma it has caused our boys", it said. "Everyone should wait until the facts come out and we know more".
"After Jordan's two brothers, Vidal and Kevon, along with their two friends, were forced to experience this tragedy up close as occupants of the vehicle, they were immediately treated as common criminals by other officers - manhandled, intimidated and arrested, while their brother lay dying in the front seat", the Edwards family said in a statement. Oliver fired an unknown number of rounds from a rifle into the moving vehicle, striking 15-year-old Jordan Edwards.
As officers left the house, the vehicle backed onto a main road and drove away despite the driver being told to stop, the new statement adds.
Friends have described Edwards as a good student and popular athlete. His 16-year-old brother was driving the vehicle, attorneys for the family say. "We anxiously await this officer's identification and arrest for the crime of murder", the family said in the statement.