A group of 20 to 30 family members and members of the Warlpiri community made the more than 1500km journey from the central Australian Aboriginal community of Yuendumu to the Darwin Supreme Court to watch the jury hand down their not guilty verdict on Friday afternoon.

They remained silent as the jury's foreperson told the court they had found Constable Zachary Rolfe not guilty of murder, as well as alternative charges of manslaughter and violent conduct causing death.

However, wailing was heard echoing out from the courthouse's foyer shortly afterwards.

Speaking to a waiting media pack, Warlpiri Elder Ned Jampijinpa Hargraves demanded "a ceasefire" in Aboriginal communities, as supporters in black t-shirts bearing the slogan "Justice for Walker '' stood behind him.

"No more guns in our communities. It must never happen again," he said.

"The police must put down their weapons...We cannot walk around in fear in our own homes."

He said now that the trial was over, his people were prepared to speak out.

"Our people have been keeping quiet because of the court process, but it is time for us to speak and tell our junga, our truth.

"We have been waiting too long for justice. We need to tell our side of this story."

Mr Walker's cousin Samara Fernandez-Brown spoke, as tears rolled down her face and supporters continued to wail, about how painful the recent years had been for her family.

"His death has affected our community in ways we could never have predicted. We are all in so much pain, particularly our young men," she said.

She said the trial had not depicted her cousin as he really was but, as Constable Rolfe's lawyer David Edwardson QC referred to him "the author of his own misfortune."

"He has been criticised and picked apart by people who did not know him, they saw only his flaws and wished to put him on trial for his own death," she said.

"We as a family and community will continue to remember him as a young man who loved animals, who loved his community and homelands, his partner, his family, his friends, and loved music.

"I know Kumanjayi would be proud of us all."

Ms Fernandez-Brown, as well as Crown prosecutor Philip Strickland SC, said there were further revelations that were not admissible in court which were set to come out in a coronial inquest later this year.

"The shooting at Yuendumu raised issues, not all of which could be explored at this trial," Mr Strickland said.

"It is our view that the family of Kumanjayi Walker and the Walpiri community and indeed the Australian people deserve no less than that full scrutiny."