Constable Zachary Rolfe was charged on Wednesday over the fatal shooting of 19-year-old Warlpiri man Kumanjayi Walker, who was shot dead at Yuendumu, about 300 kilometres from Alice Springs, on Saturday night.

Two police officers went inside a home at Yuendumu to arrest Mr Walker for alleged breaches of his suspended sentence when the fatal shooting took place.

Northern Territory Police allege Mr Walker lunged at a police officer and stabbed him with a weapon but the family disputes that version. The officers were wearing body cameras.

In a statement on Wednesday night, Northern Territory Police said a 28-year-old police officer had been charged with one count of murder. The officer was granted bail in an out-of-session court hearing, and was due to reappear in court in Alice Springs on December 19, the statement said.

"The officer has been suspended on pay," the statement said.

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

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.

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.

Northern Territory Police acting deputy commissioner Michael White said on Sunday that Mr Walker was shot after he lunged at police while armed with a weapon. One of the officers was injured in the incident.

Witnesses to the shooting have told The Age and The Sydney Morning Herald that they saw a wounded Mr Walker being dragged out of the home by his legs and thrown into the back of a police van.

One community member said a police officer was holding a gun and warning people not to come near or they would also be shot.

Mr Walker's aunty, Senita Granites, said she came back from a funeral service on Saturday and saw her nephew who "looked happy". "Thirty minutes later I heard the gunshots," she said. "I wake up in the night. I can't sleep. Everyone here in Yuendumu couldn't sleep, cause what the police done to us."

Senior Warlpiri man Ned Jampijinpa Hargraves said he felt "more relief" upon hearing the police officer was charged with murder.

"This is history," he said. "We've done it, Warlpiri have done it. I'm smiling now. It's safer for the children, I feel awesome, really great," he said .

"We'll keep fighting. Thank you for all the cities supporting, we couldn't have done it without your support."

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

The local clinic had closed the previous day because of break-ins and anti-social behaviour, meaning there was no health staff in the community to come to Mr Walker's aid.

An ambulance arrived from a neighbouring community at least an hour after the shooting, but some in the community say it was more than two hours.

Rallies were held across Australia in the four 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 in the green space between the police station and the Supreme Court, by far the town's largest building.

Several bus loads, including close family, had come in from Yuendumu and surrounding communities.

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

Senior Warlpiri man Robin Granites said another rally in Alice Springs on Thursday morning would be respectful.

"We want to show the non-Indigenous just how sorry we feel," he said. "It's not coming from our voices, it's coming from our heart. It's not to rubbish the law of the white people, but we want to show you mob what we're feeling," Mr Granites said.

"Non-Indigenous want to go around banging things, that's their business. We're here as cultural people doing it our way, in mourning ceremony."

Police in Yuendumu, who feared community reprisals, have come under fire for not informing members of the family that Mr Walker had died until the following morning. Several white people who spoke to The Age and The Sydney Morning Herald said they were told of his death on the same night as the shooting.

With an influx of community members in Alice Springs, some bottle shops are closing early for the rest of the week and are restricting their sales.

The move has been criticised as racist by some and responsible by others, including community members.

More than 500 people marched in a protest in Sydney on Wednesday that began at Town Hall and stalled with a sit-in at the Surry Hills Police Centre about 8.30pm. A NSW Police spokeswoman said no incidents were reported.

Activist Lizzie Jarrett was protesting in Sydney when the murder charge was announced and said it was "history in the making".

"We are going to take this as the win it is. Of all the hundreds of Aboriginal deaths in custody, we've never had anyone charged with the actual crime. Today is a first for our people but I can guarantee it will not be the last," she said.

Community members and family of Mr Walker called for an "independent investigation" in the aftermath of his death and requested to see police bodycam footage from Saturday. They also asked the Northern Territory Police to leave the community.

With AAP