But the Indigenous Australians minister says now is not the time for such a discussion, arguing the community should be allowed to grieve the death of the girl - whose family have asked her to be referred to as Kumanjayi Little Baby - without the tragedy being politicised.
In an opinion piece published by The Australian on Friday, coalition frontbencher Jacinta Nampijinpa Price said violence in town camps could no longer be ignored.
"Too often, difficult conversations are avoided. There is a reluctance to speak plainly about what is happening in some communities. Silence does not protect anyone," she wrote.
Town camps were established in the 1970s as a place where Indigenous people visiting from remote areas could stay for short periods, but have now become permanent homes for many.
Senator Price - who said Kumanjayi Little Baby was her niece - called for an independent inquiry into the governance of town camps, the organisations involved in their upkeep and whether current laws were protecting vulnerable Australians.
Opposition Leader Angus Taylor echoed the comments, saying the killing and subsequent reprisals were a tragedy and accusing the government of being in denial.
"You don't solve violence with more violence," he told Sky News on Friday.
"(The government needs to) get out of denial about the situation we're seeing around Alice Springs and elsewhere.
"It's the denial that has led us to this place where people aren't prepared to have honest conversations about the state of affairs in our town camps," Mr Taylor said.
Responding to the opposition's push, an emotional Indigenous Australians Minister Malarndirri McCarthy said the community needed time to heal.
"Now's not that time at all," she told ABC Radio National when asked about Senator Price's suggestion.
"Now's the time to come together as a community in sorry business and be with this mum and her son as they prepare to bury their daughter," Senator McCarthy said.
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