A Northern Territory police officer is out on bail after being charged with murder over last weekend's shooting of 19-year-old Warlpiri man Kumanjayi Walker.

Mr Walker died after he was shot at Yuendumu, a remote community 300 kilometres from Alice Springs, on Saturday night when two police officers went there to arrest him for breaches of his suspended sentence.

Constable Zachary Rolfe was released on bail after appearing in an out-of-session local court hearing on Wednesday night.

NT Police Association president Paul McCue said the officer will now be "vigorously defending the charge" against him.

Jamie Nelson Williams

"The Northern Territory Police Association acknowledges that a decorated member has now been charged with murder in relation to a critical incident at Yuendumu on Saturday, November 9," he said.

"Whilst we acknowledge the tragic circumstances of the event, the member has made it clear that he will plead not guilty and will vigorously contest the charge. He, like all, has the presumption of innocence in his favour."

The 28-year-old policeman is a former Australian Army soldier who has been awarded three bravery awards during his service with the police force.

He was awarded the National Bravery Medal in 2016 as a probationary constable after saving two tourists from floodwaters in Alice Springs.

"A 28-year-old male police officer has been charged with one count of murder over the shooting," Northern Territory police said in a statement on Wednesday.

"As this matter is before the court, no further information will be released," the statement read.

Senior Warlpiri man Ned Jampijinpa Hargraves said he felt "relief" at the decision.

"This is history. We've done it, Warlpiri have done it ... I'm smiling now," he told NITV News. "I feel awesome, really great. We'll keep fighting."

READ MORE AT NITV: Young Warlpiri man dies after being shot by Northern Territory police

The announcement about the murder charge was made after a national day of action saw hundreds of protesters take to the streets across Australia, demanding answers.

“This injustice that is happening to our people – it’s wrong,” Wiradjuri man Michael Weir told SBS News from the protest outside Parliament House in Canberra.

The grieving Yuendumu community have been calling for an independent investigation into the shooting and why it took hours for Mr Walker's family to be notified of his death.

The North Australian Aboriginal Justice Agency said on Thursday that allegations of police misconduct towards Indigenous people had "far too often been dismissed".

"It is a tragedy that it has taken the death of Kumanjayi Walker for police brutality to finally be properly scrutinised," the statement read.

SBS News

"The people of Yuendumu have demonstrated great dignity and resilience throughout these heartbreaking events. It is of vital importance that this murder charge now properly proceed through the criminal justice system. We Stand with Yuendumu."

The Northern Territory Police Commissioner Jamie Chalker has urged people to embrace rather than feel hate in a time of high tension.

"Hate should not have a place in the Northern Territory, we are renowned for how we support one another, for how we embrace one another in times of tragedy and we have had many," he said.

"Through every single one of those tragedies, the members of the Northern Territory Police, Fire and Emergency Services have been there running towards that trouble to protect you."

Constable Rolfe, who has been suspended on duty on full pay, will reappear in court on 19 December.