A proposal to restore territory rights is one step closer after a bill passed federal parliament's lower house on Wednesday.
Labor MPs Luke Gosling and Alicia Payne introduced the bill, which will ultimately allow the Northern Territory and ACT governments to legislate on voluntary assisted dying.
Prime Minister Anthony Albanese and Opposition Leader Peter Dutton allowed MPs a conscience vote on the matter.
It passed the lower house on Wednesday morning, with 99 votes for and 37 against.
The vote followed a two-day debate after the proposal was introduced to parliament on Monday.
Of the 17 MPs who spoke in the debate, 10 were in favour of the bill and seven were opposed.
Mr Gosling said he hoped the bill could be sent to the Senate for debate as soon as the next sitting period, scheduled to take place in September.
The member for the NT seat of Solomon said the passage of the bill through the lower house was a significant step forward.
"By an overwhelming margin today in the House of Representatives, our colleagues have said territorians should have the same democratic rights as those Australians living in the states," he told reporters in Canberra.
"We're hoping it receives the same support (in the Senate) as well."
The NT government passed a world-first law to legalise euthanasia in 1995, but it was short-lived.
In 1997, federal parliament passed the so-called Andrews Bill - named after former Liberal MP Kevin Andrews who introduced it - invoking a constitutional power enabling parliament to overturn territory laws.
While every state government has since passed laws to allow terminally ill adults to decide how to end their lives, the ACT and NT have been prevented from doing so.
Mr Gosling said discussions were under way with senators to ensure the bill can pass.
"The biggest message is, I guess, for senators, is that the 1995 NT legislation that was overturned by the Andrews ban is null and void," he said.
"If our bill passes the Senate, it does not come alive again, there will need to be a period of deep consultation, of drafting of legislation, should the legislative assemblies (in the NT and ACT) decide to do so."
Veterans Minister Matt Keogh was the first Labor member to oppose the bill, saying existing state legislation on voluntary assisted dying was "risky" and without appropriate safeguards.
"While I support the concept of self-government and actual self-government for our territories, in respect of this bill ... I am being asked, to exercise a Commonwealth legislative power," he told parliament on Tuesday.
"In exercising that power, (I) cannot in good conscience support this bill, so I don't."
But the bill does not legislate assisted dying but rather is about democratic equality and fairness.
Mr Gosling said there had been an "overwhelming" response from MPs in relation to the bill.
"We are hoping for a respectful debate that goes to the heart of the issue of territory rights," he said.
"If people want to treat this as a proxy vote on voluntary assisted dying, we'll continue to encourage them to look at it as an issue of democratic equality."
ACT Chief Minister Andrew Barr welcomed the bill passing the House of Representatives.
"We are in the best position we have ever been to have our rights restored," he said in a statement.
"Australia's federalism works best when all jurisdictions are treated fairly and equally."
