Mr Dutton has come under pressure to take allegations to police following a number of visits to Alice Springs to talk to local residents and journalists about high rates of violence and abuse.
Visiting the Northern Territory town last week, Mr Dutton told reporters he had brought to the prime minister's attention in October 2022 the issue of children who had been sexually abused being placed back into the hands of perpetrators.
Mr Albanese was asked on the ABC on Monday night whether in any meetings with Mr Dutton the opposition leader had put specific allegations to him.
The prime minister said he was not aware of any specific claims, but would encourage Mr Dutton to take any information to police.
NT Police Minister Kate Worden also encouraged Mr Dutton and his new Indigenous Australians spokeswoman Jacinta Price to bring forward specific claims to police.
Mr Dutton said on Tuesday he had raised "systemic issues" with Mr Albanese and was frustrated no action had been taken in the NT since he raised these issues late last year.
"There is a systemic issue in relation to some of the public servants ... the culture within the department doesn't allow them to intervene as we would in the capital cities," he told Sky News.
"I raised that with the prime minister.
"Did I say to him, 'Look, Billy Bloggs was abused at 7.03pm last Wednesday night'? No. That's not the circumstance."
He said reporting around the issue was a "distraction" from the real problems in the NT.
Mr Dutton earlier told reporters his only motivation was to work with the prime minister on solving the crisis and providing "stability" in communities like Alice Springs.
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