The Northern Territory's police minister says national silence on Indigenous deaths is contributing to a lack of funding. 

Police Minister Kate Worden says the deaths of a 40-year-old Indigenous woman and her infant child in an alleged domestic violence incident over the weekend “should be all over the news” and she is “heartbroken that it's not”. 

The bodies of a man, woman and baby were discovered on Sunday, 25 kilometres north of Alice Springs. Police say the “horrific” deaths were the result of a domestic violence incident, and that a gun was found nearby. Police have not confirmed whether or not the gun was used to kill those involved.

Ms Worden says the disturbing events show the territory's share of the national domestic violence funding pool should be calculated on need instead of population, saying “we can't hide this stuff”. 

The Northern Territory has Australia’s highest rates of domestic and family violence, with domestic violence accounting for more than 60 per cent of NT Police call outs. Indigenous women in Australia experience some of the highest rates of violence of any population in the world.

Ms Worden said Australia does not grieve the deaths of Indigenous women in the same way it grieved other deaths.

“I believe this is one reason we don't get the funding that we need,” she said.

“We have the capability to stop this. We have the capability as a community to say no more to this. But we need to work together and we need more funding.”

NT Police have not spoken publicly about some details of the crime, including whether they are investigating the deaths as a murder suicide. Police have also not been able to confirm whether anyone involved in the incident had a history of domestic violence, or if the gun found near the scene was registered.

NT-based domestic family and sexual violence researcher for ANU, Chay Brown, says the details of the incident should be released as soon as possible.

“Current guidelines ask media to – where legally possible – name acts of violence,” Dr Brown told the ABC.

She said this would allow the nation to “come together and grieve” and send a message that “the community does not tolerate acts violence”. 

NT Police Acting Commander Mark Greive says a report is being prepared for the coroner.

“Investigations into this tragedy are ongoing,” he said in a statement.

“We appreciate there is a lot of public interest, however police must maintain the integrity of the investigation and will not comment on the details.”