Leading Aboriginal organisations in the Northern Territory are calling for an “immediate and exhaustive” investigation into the police shooting death of 19-year-old Warlpiri man Kumanjayi Walker at his family home on Saturday night.

The calls came as community members and supporters protested outside Alice Springs police station for a second day to demand answers about the shooting. Another rally is scheduled for tomorrow.

Congress, the central Australian Aboriginal health service, said there were so many unanswered questions around the shooting that the inquest into Walker’s death in the town of Yuendumu should be given priority over all others and report within three months.

Quentin Walker Jurrah outside Alice Springs police station during the second day of protests. Photograph: Rhett Hammerton

The Congress CEO, Donna Ah Chee, told the rally the NT Health department should also investigate why the Yuendumu medical clinic was closed and “why it has not been immediately reopened with full services, given increase of police in the community” since the shooting.

“Clinic closures are a disturbing trend with life-threatening consequences – as we have seen this weekend,” Ah Chee said.

The Central Land Council has called for police to release the body camera footage.

“We want full transparency, we want to see the body camera evidence, we want it out in the open,” CEO, Joe Martin-Jard said.

“I call on the coroner to have this inquiry at Yuendumu and give families the chance to talk to him,” he said.

NAAJA, the Aboriginal legal service of the NT, said Walker’s death was “tragic and unnecessary”.

“The investigation of the police shooting in Yuendumu must be open, thorough and transparent and one that informs the family and community,” David Woodroffe, the service’s principal legal officer, said.

“NAAJA expects the independent coronial investigation into the death in custody to be immediate and exhaustive.”

Meanwhile, a Northern Territory MP is calling on the chief ministerto go to Yuendumu to meet with elders, as an “appropriate cultural response” to the shooting of Walker in the town, almost 300km north west of Alice Springs.

The independent member for Stuart, Scott McConnell, told ABC Radio on Monday it “would be helpful with the healing process” for Michael Gunner to sit down at Yuendumu with elders to explain how the inquiry into Walker’s death will involve them.

Organisers of Monday’s rally said they were concerned the increase in police presence in the community would only upset people further.

Walker was shot by police when they attempted to arrest him for an outstanding warrant. They took him to the police station, where he died while waiting for medical assistance to arrive.

His family were not told of his death on Saturday night.

Senior police officers visited the community on Sunday to speak to residents, who had been remarkably calm, McConnell said, despite their distress.

“There has been incredibly good leadership from elders who kept people calm in an absolute vacuum of information [from police],” McConnell said.

He said the government and the NT police needed to “explain and justify the inquiry” they were undertaking because “the community don’t believe it is independent enough and I support them in that”.

The health clinic was closed over the weekend, meaning there were no medical staff in the community at the time of the shooting. McConnell said the closure of the health clinic was an “inadequate” response to the needs of Yuendumu.

“Yuendumu is a difficult place to live and work at the moment. We do have an issue with law and order and crime in the NT, and I have been concerned about these things for a long time,” McConnell said. “I feel for health staff at Yuendumu … but the government’s response to that seem to have been inadequate.

“The police station has never been fully operational and [the government] is too willing to close community clinics. It’s not a minor community, it’s 1,000 people. The citizens of Yuendumu need to be kept safe with their clinic kept open.”

The clinic will open today during business hours, staffed by workers from nearby Yuelamu.

A spokesman for the chief minister said Gunner would visit “subject to consultation with the family and community leaders”.