“If Senator Price has any evidence whatsoever that is occurring within the system she needs to come forward and make a mandatory report,” she told reporters on Sunday.

Worden defended the territory’s foster care system,which she said aimed to find places for children to live in their family or in their culture “but never at the expense of the safety of the child”.

“It is not a system that places children back into the care of perpetrators,” she said.

Price said Worden would be aware of the “failures of her department” if she had listened to warnings from foster parents.

“Peter Dutton and I listened to the stories from people on the ground of the failures of the Northern Territory government and the Territory Families department,failures that they have already reported and which have gone unaddressed or have been mishandled.

Price backed Dutton’s call for a royal commission into the sexual abuse of Indigenous children. She said evidence of child abuse had been reported but the Northern Territory government was continuing to place children with abusers.

She also supported states and territories handing over control of child protection.

“It is incumbent upon state and territory governments to do the right thing when it comes to child protection ... and the only sort of referendum I would support right now is if we put the lives and the responsibility of children into the federal arena.

“That’s a referendum I could get behind because I think we absolutely need a review of how that is or isn’t working across the board.”

Price and Dutton this week ramped up their No campaign,claiming the government’s proposal to change the constitution to enshrine a Voice to parliament lacks detail,is racially divisive and will fail to amplify concerns of the regional and remote Indigenous people it seeks to empower.

Prime Minister Anthony Albanese remains optimistic about the potential for a referendum to approve the amendments to the constitution needed to establish the Voice.

He will speak on Monday at the launch of former Liberal MP and ultra-marathon runner Pat Farmer’s 14,400-kilometre run around Australia to raise support for the Voice.

“Australians everywhere are responding to the gracious,generous,patient invitation of the Uluru Statement from the Heart with their own instinctive fairness and decency,” he will say.

“It’s why I have always been optimistic about this referendum – because I’ve always been optimistic about the generosity of the Australian people.”

Cut through the noise of federal politics with news,views and expert analysis from Jacqueline Maley. Subscribers can sign up to our weeklyInside Politics newsletter here.