Justine Damond, 40, was shot in July as she approached a police car in her pajamas after placing an emergency call reporting a possible rape near her home in Minnesota.
Hennepin County Attorney Mike Freeman said last week investigators looking into her death "haven't done their job" and he lacked sufficient evidence to prosecute officer Mohamed Noor, who shot and killed her.
Damond's family said they felt the need to speak out publicly after Freeman's comments, and called on American prosecutors to keep pursuing the case.
"We are deeply concerned that the initial investigation was not done properly and with the greatest of integrity and sense of completeness," Damond's father John Ruszczyk told reporters in Sydney.
"Ignorance cannot prevail here. We implore Mr Freeman and the prosecutor's office to continue to rigorously review an examination of the evidence that led to Justine's death."
He added that the family would "wait patiently" for the review to be completed but pleaded for it to be "done right".
Freeman made the unguarded comments at a holiday party last Wednesday evening when approached by a group that videotaped the interaction and posted it on Facebook.
"I've got to have the evidence, and I don't have it yet," Freeman said.
He said Noor has been uncooperative, refusing to speak with investigators, and that his partner Matthew Harrity did not provide useful evidence.
"Let me just say it's not my fault. So if it isn't my fault, who didn't do their job? Investigators. They don't work for me. They haven't done their job."
Widespread protests and criticism of the shooting led to the resignation of Minneapolis police chief Janee Harteau.
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