Anne Ruston won't back a repeal of the Andrews Bill until legislation is put to parliament but says all Australians "should be equal" under the law.
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The Coalition health spokeswoman has told The Canberra Times parliament "shouldn't be afraid" to debate the move, which would pave the way for the ACT and NT to legislate voluntary assisted dying.
Ms Ruston said she would be "very keen" to seek the views of territorians, currently barred from legislating voluntary assisted dying, but stopped short of backing the proposal without assessing legislation put to parliament.
"I believe that every Australian in the eyes of every government in Australia should be equal, and I don't move away from that as an underlying principle," she said.
"But there are often issues of complication that occur in legislation and I would like to see the actual legislation."
Labor backbenchers Alicia Payne, from the ACT, and Luke Gosling, from the NT, have flagged intent to bring legislation overturning the 25-year-old ban before parliament as early as this month.
Ms Ruston was one of a number of senators to reverse their support for the 2018 Restoring Territory Rights Bill, consigning it to a shock defeat by just two votes.
The reversal came after intense lobbying from groups opposed to voluntary assisted dying, which had only been legislated by Victoria at the time.
But every state has since passed laws to legalise voluntary euthanasia, leaving the territories as the only jurisdictions where it remained outlawed.
Ms Ruston said she could understand the frustrations of territorians, urging parliament not to shy away from "robust debate".
"They're sensitive issues. They often have polarising views amongst people. That's what the parliament's here for," she said.
"What I often do with conscious legislation ... is seek the views of of my own electorate, and equally I'll be very keen to seek the views of the people that live in the NT and the ACT."
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The Coalition, under former Prime Minister Scott Morrison, opposed repealing the Andrews Bill, implemented in 1995 when the NT attempted to legalise voluntary assisted dying.
But Coalition Senate leader Simon Birmingham, a supporter of removing the bill, was now working to ensure its repeal was debated in the upper house.
Prime Minister Anthony Albanese has long supported the repealing the bill, and has promised a conscience vote on the matter. But he would not be drawn on a timetable two days before winning the May 21 election.
New ACT senator David Pocock has also pledged to introduce a private member's bill in the first weeks of the new parliament, set to sit from July 26.