Chief Minister Andrew Barr is cautiously optimistic the territory rights bill will become law, paving the way for the ACT government to consider assisted dying laws.
The private members' bill, which would remove a 25-year ban on the territories legislating voluntary euthanasia, was introduced to the Senate on Monday after passing the lower house in early August.
After a 2018 attempt to overturn the so-called Andrews Bill failed in the Senate, Mr Barr insisted he was not taking the result "for granted".
But he said he was "cautiously" optimistic the bill would pass, arguing the dynamics had shifted significantly in the intervening period.
"We've been down this path before with the Senate and the bill was defeated by one vote in a previous parliament," Mr Barr told the ABC's RN on Tuesday.
"[But] obviously, the composition of the Senate has changed since that time, so I think there is reason for optimism."
Prime Minister Anthony Albanese, who supported the Restoring Territory Rights Bill in the lower house, has allowed a conscience vote and a number of Labor members will oppose the move.
One of those was Labor senator and Catholic Deborah O'Neill, who has stressed the need for a faith perspective in the debate.
Mr Barr suspected religious opposition to the bill was less prevalent than during previous attempts to overturn the Andrews Bill, but conceded it remained "a question".
The push was bolstered by the arrival of ACT independent senator David Pocock, a supporter of repealing the ban, saying residents of the territories are "second class citizens".
Senator Pocock ousted Liberal and hardline conservative Zed Seselja, a staunch opponent of voluntary assisted dying.
The Manager of Government Business in the Senate and ACT Senator Katy Gallagher, previously told The Canberra Times that she was "very optimistic" and the bill was territory rights' "best shot" although she said senate numbers are "very tight".
The Senate was unlikely to hold a vote until the end of the year.
The 1997 Andrews Bill overturned the Northern Territory's 1995 world-first voluntary euthanasia regime. Since then, every Australian state has legislated voluntary assisted dying, leaving the two territories as the outliers.
Mr Barr said it had been on the ACT government's agenda for "a number of parliaments", with its own legislation and a 2019 inquiry into end of life choices running parallel to federal attempts to overturn the Andrews Bill.
He said the ACT government would rely on the six other state's assisted dying legislation and consultations to draft their own bill.
"It would be the ACT government's intention to commence that process and hopefully conclude it, subject of course to the deliberations of our parliament, where I imagine it will be a conscience vote for every single member," he said.