A bill to overturn a 25-year-old ban on the ACT and the Northern Territory legislating voluntary assisted dying could be brought before federal parliament within weeks.
Labor backbenchers Alicia Payne, from Canberra, and Luke Gosling, from Darwin, plan to table legislation at the next parliamentary sitting to remove the Commonwealth veto.
However, the Albanese government will allow Labor parliamentarians a conscience vote rather than direct them to support the bill.
The Coalition also allows its members a free vote on euthanasia, meaning the bill's success is not guaranteed.
In May, New South Wales became the last Australian state to allow terminally ill adults to choose how to end their lives.
However, the so-called "Andrews Bill", passed in federal parliament in 1997, still prevents the NT and ACT from making similar laws.
In 1995, the NT established the world's first legal euthanasia regime.
The following year, Darwin man Bob Dent, who had terminal prostate cancer, become the first person to die via state-sanctioned voluntary euthanasia.
His controversial death prompted then Liberal backbencher Kevin Andrews to gain federal parliament's support to invoke the Commonwealth's rarely used constitutional power to overturn territory laws.
'Senate has now changed' after failed past attempts to ditch Andrews Bill
Minor parties have attempted to revoke the Andrews Bill three times — in 2008, 2010 and 2018 — but conscience votes saw each attempt defeated in the Senate.
The last bill, sponsored by then Liberal Democrat senator David Leyonhjelm, fell two votes short of passing.
However, Ms Payne told the ABC she believed that views among senators, and within her own party, had changed since then.
She said former ACT Liberal senator Zed Seselja's historic loss in May — he became the first territory senator to lose his seat at an election — was a measure of how strongly voters felt.
"It just resonated so much with Canberrans that they had a senator who didn't want to support them having an equal democratic right as our neighbours in Queanbeyan [across the NSW border]," she said.
"And I think that was a really key issue in the last election."
Conscience vote unnecessary for federal parliamentarians, says Pocock
On the weekend, independent ACT senator David Pocock, who unseated Mr Seselja in this year's election, urged Labor to remove the Andrews Bill without a conscience vote.
Senator Pocock, who championed territory rights in his election campaign, said there was no need for another prolonged federal debate.
"Every state has now legislated on voluntary assisted dying," he told the ABC's Insiders program.
However, Ms Payne said Labor was applying a conscience vote because the Andrews Bill related solely to euthanasia, rather than territory rights more broadly.
"And I really deeply respect the right of my colleagues to have a conscience view on that issue," she said.
Ms Payne said she and Mr Gosling believed there was strong support for the bill within the Labor Party, but would discuss it with all parliamentarians in the lead-up to the debate.
