Ms Siewert said Indigenous legal services and family violence services were too important to receive cuts.
"Mr Abbott talks big about putting ATI issues first but then what does he do? Some of his first moves are cuts," she said.
The Greens believe Mr Abbott will trim budget spending from a wide range of essential services as his first option of recouping budgetary funds.
"Now everybody knows that incarceration rates of Indigenous youths is just appalling and we need to be addressing that," Ms Siewert said.
“We need to be of course looking at justice reinvestment and how we stop people entering the justice system in the first place. The legal system is not the area it should be cut."
Mr Abbott declared he would place Indigenous issues high on his list of priorities at the start of his term.
The reduction of funding to Indigenous legal services was supported by Indigenous Advisory Council head, Warren Mundine.
Ms Siewert said this was unacceptable.
"He's supposed to be in there defending and making sure that money is allocated to Aboriginal and TI issues," she said of Mr Mundine.
"I also question some of the comments that he made last week around pragmatism and ideology."
Ms Siewert was referring to an article written by Mr Mundine in which he commented: "Too often, vocal activism on indigenous issues is dominated by ideologies."