Former Canberra man, Constable Zachary Rolfe, 28, was charged on Wednesday over the fatal shooting of 19-year-old Warlpiri man Kumanjayi Walker after he and another police officer went inside a home at Yuendumu, about 300 kilometres from Alice Springs, to arrest Mr Walker for alleged breaches of his suspended sentence.

The Northern Territory Police Association on Thursday afternoon released a statement saying the "decorated member" had "made it clear he will plead not guilty and vigorously contest the charge", and that Constable Rolfe and his family had the association's complete support.

"He, like all, has the presumption of innocence in his favour," the statement said.

The Warlpiri people have called for Constable Rolfe's trial to be held locally in the remote town of Yuendumu. Thousands of Indigenous and non-Indigenous Australians attended a rally on Thursday in Alice Springs to demand justice for the 19-year-old.

Northern Territory Police alleges Mr Walker lunged at a police officer and stabbed him with a weapon but the family disputes that version.

Witnesses have said they saw a wounded Mr Walker being dragged out of the home and thrown into the back of a police van. The officers were wearing body cameras.

Constable Rolfe was granted bail in an out-of-session court hearing, and is due to reappear in court in Alice Springs on December 19. He has been suspended by Northern Territory Police with pay.

Northern Territory Chief Minister Michael Gunner on Thursday said he was "experiencing all of the gamut of emotions".

"This is an incredibly sad time for all. It is a time of high emotion. There are many people hurting in Yuendumu and around the Northern Territory and in our police force," Mr Gunner said.

As Territorians we have been through challenging times before, we cannot and will not let this divide us."

At Thursday's rally, Indigenous Australians walked in painted and wailing, a mourning procession rarely seen outside Aboriginal communities.

"I want to make it clear it's a very sad day, black or white," senior Warlpiri man Robin Granites told the crowd.

The rally moved through the streets of Alice Springs chanting "we want justice for Walker". It was mostly peaceful, but some threw water bottles at the monstrous Supreme Court building.

The rally ended at the heavily guarded police station, where tempers threatened to boil over before elders calmed down a handful of angry young men.

The crowd, including senior grieving women, became upset when former NT politician Bess Price, flanked by daughter Jacinta, took the microphone.

The Prices, who have been vocal about domestic violence in remote Australia, decried the "hypocrisy" of Warlpiri communities before being met by boos and howls from the crowd.

Speeches from elders became increasingly emotional as the rally went on. There were tears and screams over the microphone railing against white control of the justice system, politics and Aboriginal organisations.

"Our history will break this," said one speaker, pointing to the police station.

Protesters asked how, when an Aboriginal man may be locked up for months for stealing a bottle of wine, a police officer charged with murder could be granted bail.

Federal shadow minister for Indigenous Australians Linda Burney told ABC radio there was "enormous surprise" in the community that bail had been granted following the murder charge.

Ms Burney said Mr Walker's family was calling for an independent and thorough investigation.

"The most important thing the family is asking for is calm and respect," she said.

Mr Gunner would not be drawn on the particulars of the shooting while the case was before the courts, but gave assurances the investigation would be independent. The coroner and the Independent Commission Against Corruption are also overseeing the case.

Mr Gunner said his priority was keeping critical services open, with the Yuendumu school up and running and extra classrooms open in Alice Springs while the community heads there for protests.

"It is my priority, as Chief Minister, it is my job, to try to make sure that the Territory goes through a healing processs and we return to normal as soon as possible."

Indigenous Australians Minister Ken Wyatt, who travelled to the Alice Springs to speak with the community and Chief Minister, said "now is not the time for blame ... it is a time for compassion."

"I understand that these are difficult and emotional times for many members of the community. My thoughts are with all those directly involved and their families, as well as the broader community," Mr Wyatt said in a statement on Thursday.

Constable Rolfe is the son of well-known Canberra businesspeople and philanthropists Debbie and Richard Rolfe. The former Canberra Grammar student and Australian Army officer joined the Northern Territory Police in 2016.

Earlier this year he received the Royal Humane Society's highest bravery award for rescuing two international tourists from a flood-swollen river in the Northern Territory in 2016.

Mr Walker's death has become a flashpoint for Australian race relations and the servicing of remote communities.

Rallies have been held across Australia in the days since the shooting, including in Canberra, Darwin, Melbourne and Sydney.

In Alice Springs on Wednesday night, several hundred people staged a peaceful candlelight vigil.

News of the murder charge was announced over the microphone about 7.30pm local time on Wednesday to rapturous cheers and clapping.

Speaking to reporters on Thursday morning, Ms Burney said there was a broader issue of poverty and lack of essential services for people in the Northern Territory.

"I think the way I feel is the way that many people feel, and that's a level of frustration in the sense of listenting to Aboriginal people, making sure that the appropriate services in communities and ... understanding what the challenges are for people that live in remote Australia."